Daily Papers

In RL, given a prompt, we sample a group of completions from a model and score them. Two questions follow: which completions should gain probability mass, and how should the parameters move to realize that change? Standard policy-gradient methods answer both at once, so the update can overshoot or undershoot depending on the learning rate, clipping, and other optimizer choices. We introduce Target Policy Optimization (TPO), which separates the two questions. Given scored completions, TPO constructs a target distribution q_i propto p_i^{,old} exp(u_i) and fits the policy to it by cross-entropy. The loss gradient on sampled-completion logits is p^θ- q, which vanishes once the policy matches the target. On tabular bandits, transformer sequence tasks, and billion-parameter LLM RLVR, TPO matches PG, PPO, GRPO, and DG on easy tasks and substantially outperforms them under sparse reward. Code is available at https://github.com/JeanKaddour/tpo.

Cascading bandits have gained popularity in recent years due to their applicability to recommendation systems and online advertising. In the cascading bandit model, at each timestep, an agent recommends an ordered subset of items (called an item list) from a pool of items, each associated with an unknown attraction probability. Then, the user examines the list, and clicks the first attractive item (if any), and after that, the agent receives a reward. The goal of the agent is to maximize the expected cumulative reward. However, the prior literature on cascading bandits ignores the influences of user states (e.g., historical behaviors) on recommendations and the change of states as the session proceeds. Motivated by this fact, we propose a generalized cascading RL framework, which considers the impact of user states and state transition into decisions. In cascading RL, we need to select items not only with large attraction probabilities but also leading to good successor states. This imposes a huge computational challenge due to the combinatorial action space. To tackle this challenge, we delve into the properties of value functions, and design an oracle BestPerm to efficiently find the optimal item list. Equipped with BestPerm, we develop two algorithms CascadingVI and CascadingBPI, which are both computationally-efficient and sample-efficient, and provide near-optimal regret and sample complexity guarantees. Furthermore, we present experiments to show the improved computational and sample efficiencies of our algorithms compared to straightforward adaptations of existing RL algorithms in practice.

In this paper, we introduce the Preselection Bandit problem, in which the learner preselects a subset of arms (choice alternatives) for a user, which then chooses the final arm from this subset. The learner is not aware of the user's preferences, but can learn them from observed choices. In our concrete setting, we allow these choices to be stochastic and model the user's actions by means of the Plackett-Luce model. The learner's main task is to preselect subsets that eventually lead to highly preferred choices. To formalize this goal, we introduce a reasonable notion of regret and derive lower bounds on the expected regret. Moreover, we propose algorithms for which the upper bound on expected regret matches the lower bound up to a logarithmic term of the time horizon.

Nash regret has recently emerged as a principled fairness-aware performance metric for stochastic multi-armed bandits, motivated by the Nash Social Welfare objective. Although this notion has been extended to linear bandits, existing results suffer from suboptimality in ambient dimension d, stemming from proof techniques that rely on restrictive concentration inequalities. In this work, we resolve this open problem by introducing new analytical tools that yield an order-optimal Nash regret bound in linear bandits. Beyond Nash regret, we initiate the study of p-means regret in linear bandits, a unifying framework that interpolates between fairness and utility objectives and strictly generalizes Nash regret. We propose a generic algorithmic framework, FairLinBandit, that works as a meta-algorithm on top of any linear bandit strategy. We instantiate this framework using two bandit algorithms: Phased Elimination and Upper Confidence Bound, and prove that both achieve sublinear p-means regret for the entire range of p. Extensive experiments on linear bandit instances generated from real-world datasets demonstrate that our methods consistently outperform the existing state-of-the-art baseline.

Multi-armed bandits a simple but very powerful framework for algorithms that make decisions over time under uncertainty. An enormous body of work has accumulated over the years, covered in several books and surveys. This book provides a more introductory, textbook-like treatment of the subject. Each chapter tackles a particular line of work, providing a self-contained, teachable technical introduction and a brief review of the further developments; many of the chapters conclude with exercises. The book is structured as follows. The first four chapters are on IID rewards, from the basic model to impossibility results to Bayesian priors to Lipschitz rewards. The next three chapters cover adversarial rewards, from the full-feedback version to adversarial bandits to extensions with linear rewards and combinatorially structured actions. Chapter 8 is on contextual bandits, a middle ground between IID and adversarial bandits in which the change in reward distributions is completely explained by observable contexts. The last three chapters cover connections to economics, from learning in repeated games to bandits with supply/budget constraints to exploration in the presence of incentives. The appendix provides sufficient background on concentration and KL-divergence. The chapters on "bandits with similarity information", "bandits with knapsacks" and "bandits and agents" can also be consumed as standalone surveys on the respective topics.

Contextual dueling bandits, where a learner compares two options based on context and receives feedback indicating which was preferred, extends classic dueling bandits by incorporating contextual information for decision-making and preference learning. Several algorithms based on the upper confidence bound (UCB) have been proposed for linear contextual dueling bandits. However, no algorithm based on posterior sampling has been developed in this setting, despite the empirical success observed in traditional contextual bandits. In this paper, we propose a Thompson sampling algorithm, named FGTS.CDB, for linear contextual dueling bandits. At the core of our algorithm is a new Feel-Good exploration term specifically tailored for dueling bandits. This term leverages the independence of the two selected arms, thereby avoiding a cross term in the analysis. We show that our algorithm achieves nearly minimax-optimal regret, i.e., mathcal{O}(dsqrt T), where d is the model dimension and T is the time horizon. Finally, we evaluate our algorithm on synthetic data and observe that FGTS.CDB outperforms existing algorithms by a large margin.

Dueling bandits is a prominent framework for decision-making involving preferential feedback, a valuable feature that fits various applications involving human interaction, such as ranking, information retrieval, and recommendation systems. While substantial efforts have been made to minimize the cumulative regret in dueling bandits, a notable gap in the current research is the absence of regret bounds that account for the inherent uncertainty in pairwise comparisons between the dueling arms. Intuitively, greater uncertainty suggests a higher level of difficulty in the problem. To bridge this gap, this paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM). We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound tilde Obig(dsum_{t=1^Tsigma_t^2} + dbig), where sigma_t is the variance of the pairwise comparison in round t, d is the dimension of the context vectors, and T is the time horizon. Our regret bound naturally aligns with the intuitive expectation in scenarios where the comparison is deterministic, the algorithm only suffers from an tilde O(d) regret. We perform empirical experiments on synthetic data to confirm the advantage of our method over previous variance-agnostic algorithms.

We advance the study of incentivized bandit exploration, in which arm choices are viewed as recommendations and are required to be Bayesian incentive compatible. Recent work has shown under certain independence assumptions that after collecting enough initial samples, the popular Thompson sampling algorithm becomes incentive compatible. We give an analog of this result for linear bandits, where the independence of the prior is replaced by a natural convexity condition. This opens up the possibility of efficient and regret-optimal incentivized exploration in high-dimensional action spaces. In the semibandit model, we also improve the sample complexity for the pre-Thompson sampling phase of initial data collection.

We study contextual combinatorial bandits with probabilistically triggered arms (C^2MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C^2-UCB-T algorithm and propose a novel analysis that achieves an O(dKT) regret bound, removing a potentially exponentially large factor O(1/p_{min}), where d is the dimension of contexts, p_{min} is the minimum positive probability that any arm can be triggered, and batch-size K is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC^2-UCB and derive a regret bound O(dT), which is independent of the batch-size K. As a valuable by-product, our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C^2MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets.

We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. Extensive simulations demonstrate the improved performance of our proposed algorithm over existing ones.

The goal of this thesis is to investigate the structural properties of certain sequential problems in order to bring the solutions closer to a practical use. In the first part, we put a special emphasis on structures that can be represented as graphs on actions. In the second part, we study the large action spaces that can be of exponential size in the number of base actions or even infinite. For graph bandits, we consider the settings of smoothness of rewards (spectral bandits), side observations, and influence maximization. For large structured domains, we cover kernel bandits, polymatroid bandits, bandits for function optimization (including unknown smoothness), and infinitely many-arms bandits. The thesis aspires to be a survey of the author's contributions on graph and structured bandits.

We consider a combinatorial multi-armed bandit problem for maximum value reward function under maximum value and index feedback. This is a new feedback structure that lies in between commonly studied semi-bandit and full-bandit feedback structures. We propose an algorithm and provide a regret bound for problem instances with stochastic arm outcomes according to arbitrary distributions with finite supports. The regret analysis rests on considering an extended set of arms, associated with values and probabilities of arm outcomes, and applying a smoothness condition. Our algorithm achieves a O((k/Delta)log(T)) distribution-dependent and a O(T) distribution-independent regret where k is the number of arms selected in each round, Delta is a distribution-dependent reward gap and T is the horizon time. Perhaps surprisingly, the regret bound is comparable to previously-known bound under more informative semi-bandit feedback. We demonstrate the effectiveness of our algorithm through experimental results.

Motivated by the phenomenon of strategic agents gaming a recommender system to maximize the number of times they are recommended to users, we study a strategic variant of the linear contextual bandit problem, where the arms can strategically misreport privately observed contexts to the learner. We treat the algorithm design problem as one of mechanism design under uncertainty and propose the Optimistic Grim Trigger Mechanism (OptGTM) that incentivizes the agents (i.e., arms) to report their contexts truthfully while simultaneously minimizing regret. We also show that failing to account for the strategic nature of the agents results in linear regret. However, a trade-off between mechanism design and regret minimization appears to be unavoidable. More broadly, this work aims to provide insight into the intersection of online learning and mechanism design.

This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a parameter estimation routine that sequentially estimates a set of base-arm parameters, and (2) a super-arm selection policy for selecting a subset of base arms deemed optimal based on these parameters. State-of-the-art algorithms assume access to an exact oracle for super-arm selection with unbounded computational power. At each instance, this oracle evaluates a list of score functions, the number of which grows as low as linearly and as high as exponentially with the number of arms. This can be prohibitive in the regime of a large number of arms. This paper introduces a novel realistic alternative to the perfect oracle. This algorithm uses a combination of group-testing for selecting the super arms and quantized Thompson sampling for parameter estimation. Under a general separability assumption on the reward function, the proposed algorithm reduces the complexity of the super-arm-selection oracle to be logarithmic in the number of base arms while achieving the same regret order as the state-of-the-art algorithms that use exact oracles. This translates to at least an exponential reduction in complexity compared to the oracle-based approaches.

Fast changing states or volatile environments pose a significant challenge to online optimization, which needs to perform rapid adaptation under limited observation. In this paper, we give query and regret optimal bandit algorithms under the strict notion of strongly adaptive regret, which measures the maximum regret over any contiguous interval I. Due to its worst-case nature, there is an almost-linear Omega(|I|^{1-epsilon}) regret lower bound, when only one query per round is allowed [Daniely el al, ICML 2015]. Surprisingly, with just two queries per round, we give Strongly Adaptive Bandit Learner (StABL) that achieves O(n|I|) adaptive regret for multi-armed bandits with n arms. The bound is tight and cannot be improved in general. Our algorithm leverages a multiplicative update scheme of varying stepsizes and a carefully chosen observation distribution to control the variance. Furthermore, we extend our results and provide optimal algorithms in the bandit convex optimization setting. Finally, we empirically demonstrate the superior performance of our algorithms under volatile environments and for downstream tasks, such as algorithm selection for hyperparameter optimization.

We introduce a practical, black-box framework termed Detection Augmented Learning (DAL) for the problem of piecewise stationary bandits without knowledge of the underlying non-stationarity. DAL accepts any stationary bandit algorithm with order-optimal regret as input and augments it with a change detector, enabling applicability to all common bandit variants. Extensive experimentation demonstrates that DAL consistently surpasses all state-of-the-art methods across diverse non-stationary scenarios, including synthetic benchmarks and real-world datasets, underscoring its versatility and scalability. We provide theoretical insights into DAL's strong empirical performance, complemented by thorough empirical validation.

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear alpha-regret methods that only require bandit feedback, achieving Oleft(T^2{3}log(T)^1{3}right) expected cumulative alpha-regret dependence on the horizon T. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to multiple problems in submodular maximization, adapting approximation algorithms for cardinality and for knapsack constraints. The new CMAB algorithms for knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.

We consider adversarial multi-armed bandit problems where the learner is allowed to observe losses of a number of arms beside the arm that it actually chose. We study the case where all non-chosen arms reveal their loss with a fixed but unknown probability r, independently of each other and the action of the learner. We propose two algorithms that work for different ranges of r. We show that after T rounds in a bandit problem with N arms, the expected regret of our first algorithm is O((T /r) log N ) whenever rge(log T)/(2N), while our second algorithm achieves a regret of O((T/r) log (N+T)) for smaller values of r. We also give a quick estimation procedure that decides the range of~r. All our bounds are within logarithmic factors of the best achievable performance of any algorithm that is even allowed to know~r.

In machine learning, the notion of multi-armed bandits refers to a class of online learning problems, in which an agent is supposed to simultaneously explore and exploit a given set of choice alternatives in the course of a sequential decision process. In the standard setting, the agent learns from stochastic feedback in the form of real-valued rewards. In many applications, however, numerical reward signals are not readily available -- instead, only weaker information is provided, in particular relative preferences in the form of qualitative comparisons between pairs of alternatives. This observation has motivated the study of variants of the multi-armed bandit problem, in which more general representations are used both for the type of feedback to learn from and the target of prediction. The aim of this paper is to provide a survey of the state of the art in this field, referred to as preference-based multi-armed bandits or dueling bandits. To this end, we provide an overview of problems that have been considered in the literature as well as methods for tackling them. Our taxonomy is mainly based on the assumptions made by these methods about the data-generating process and, related to this, the properties of the preference-based feedback.

Web-based applications such as chatbots, search engines and news recommendations continue to grow in scale and complexity with the recent surge in the adoption of LLMs. Online model selection has thus garnered increasing attention due to the need to choose the best model among a diverse set while balancing task reward and exploration cost. Organizations faces decisions like whether to employ a costly API-based LLM or a locally finetuned small LLM, weighing cost against performance. Traditional selection methods often evaluate every candidate model before choosing one, which are becoming impractical given the rising costs of training and finetuning LLMs. Moreover, it is undesirable to allocate excessive resources towards exploring poor-performing models. While some recent works leverage online bandit algorithm to manage such exploration-exploitation trade-off in model selection, they tend to overlook the increasing-then-converging trend in model performances as the model is iteratively finetuned, leading to less accurate predictions and suboptimal model selections. In this paper, we propose a time-increasing bandit algorithm TI-UCB, which effectively predicts the increase of model performances due to finetuning and efficiently balances exploration and exploitation in model selection. To further capture the converging points of models, we develop a change detection mechanism by comparing consecutive increase predictions. We theoretically prove that our algorithm achieves a logarithmic regret upper bound in a typical increasing bandit setting, which implies a fast convergence rate. The advantage of our method is also empirically validated through extensive experiments on classification model selection and online selection of LLMs. Our results highlight the importance of utilizing increasing-then-converging pattern for more efficient and economic model selection in the deployment of LLMs.

We study a strategic variant of the multi-armed bandit problem, which we coin the strategic click-bandit. This model is motivated by applications in online recommendation where the choice of recommended items depends on both the click-through rates and the post-click rewards. Like in classical bandits, rewards follow a fixed unknown distribution. However, we assume that the click-rate of each arm is chosen strategically by the arm (e.g., a host on Airbnb) in order to maximize the number of times it gets clicked. The algorithm designer does not know the post-click rewards nor the arms' actions (i.e., strategically chosen click-rates) in advance, and must learn both values over time. To solve this problem, we design an incentive-aware learning algorithm, UCB-S, which achieves two goals simultaneously: (a) incentivizing desirable arm behavior under uncertainty; (b) minimizing regret by learning unknown parameters. We characterize all approximate Nash equilibria among arms under UCB-S and show a mathcal{O} (KT) regret bound uniformly in every equilibrium. We also show that incentive-unaware algorithms generally fail to achieve low regret in the strategic click-bandit. Finally, we support our theoretical results by simulations of strategic arm behavior which confirm the effectiveness and robustness of our proposed incentive design.

In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance tau. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is Omega(tau^{-1AK}), where A is the number of actions and K is the number of episodes, and that it is achieved by an Upper Confidence Bound algorithm with a novel Bernstein bonus. For online RL in tabular Markov Decision Processes (MDPs), we show a minimax regret lower bound of Omega(tau^{-1SAK}) (with normalized cumulative rewards), where S is the number of states, and we propose a novel bonus-driven Value Iteration procedure. We show that our algorithm achieves the optimal regret of widetilde O(tau^{-1SAK}) under a continuity assumption and in general attains a near-optimal regret of widetilde O(tau^{-1}SAK), which is minimax-optimal for constant tau. This improves on the best available bounds. By discretizing rewards appropriately, our algorithms are computationally efficient.

Tabular data generation has become increasingly essential for enabling robust machine learning applications, which require large-scale, high-quality data. Existing solutions leverage generative models to learn original data distributions. However, real-world data are naturally heterogeneous with diverse distributions, making it challenging to obtain a universally good model for diverse data generation. To address this limitation, we introduce Diversity-Aware Tabular data gEnerator (DATE), a framework that (i) prepares high-quality and distributionally distinct examples for in-context learning by effectively partitioning the original heterogeneous data into multiple diverse subsets; (ii) harnesses Large Language Models (LLMs) to explore the diversity of the partitioned distribution with decision tree reasoning as feedback, generating high-quality labeled data for each subset. However, the massive generated data inherently involves a trade-off between diversity and quality. To integrate this issue, existing solutions greedily select the validation-best data. However, we prove that the selection in heterogeneous settings does not possess the greedy-choice property, and design a Multi-Arm Bandit-based sampling algorithm that balances the diversity and quality of generated data. Extensive experiments on tabular classification and regression benchmarks demonstrate that DATE consistently outperforms state-of-the-art GAN-based and LLM-based methods. On average, DATE achieves a 23.75% reduction in error rate with just 100 generated data. Empirically, we demonstrate that data generated by DATE can improve the accuracy of Direct Preference Optimization (DPO) and enhance the reasoning capability of LLMs on the target data. Code is available at https://github.com/windblow32/DATE.

We consider the combinatorial bandits problem with semi-bandit feedback under finite sampling budget constraints, in which the learner can carry out its action only for a limited number of times specified by an overall budget. The action is to choose a set of arms, whereupon feedback for each arm in the chosen set is received. Unlike existing works, we study this problem in a non-stochastic setting with subset-dependent feedback, i.e., the semi-bandit feedback received could be generated by an oblivious adversary and also might depend on the chosen set of arms. In addition, we consider a general feedback scenario covering both the numerical-based as well as preference-based case and introduce a sound theoretical framework for this setting guaranteeing sensible notions of optimal arms, which a learner seeks to find. We suggest a generic algorithm suitable to cover the full spectrum of conceivable arm elimination strategies from aggressive to conservative. Theoretical questions about the sufficient and necessary budget of the algorithm to find the best arm are answered and complemented by deriving lower bounds for any learning algorithm for this problem scenario.

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order O(H^3SAT) where H is the length of one episode, S is the number of states, A the number of actions, T the number of episodes, that matches the lower-bound of Ω(H^3SAT) up to poly-log terms in H,S,A,T for a large enough T. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon H (and S) without the need for an involved Bernstein-like bonus or noise. Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin, 1981).

We improve the efficiency of algorithms for stochastic combinatorial semi-bandits. In most interesting problems, state-of-the-art algorithms take advantage of structural properties of rewards, such as independence. However, while being optimal in terms of asymptotic regret, these algorithms are inefficient. In our paper, we first reduce their implementation to a specific submodular maximization. Then, in case of matroid constraints, we design adapted approximation routines, thereby providing the first efficient algorithms that rely on reward structure to improve regret bound. In particular, we improve the state-of-the-art efficient gap-free regret bound by a factor m/log m, where m is the maximum action size. Finally, we show how our improvement translates to more general budgeted combinatorial semi-bandits.

We consider stochastic sequential learning problems where the learner can observe the average reward of several actions. Such a setting is interesting in many applications involving monitoring and surveillance, where the set of the actions to observe represent some (geographical) area. The importance of this setting is that in these applications, it is actually cheaper to observe average reward of a group of actions rather than the reward of a single action. We show that when the reward is smooth over a given graph representing the neighboring actions, we can maximize the cumulative reward of learning while minimizing the sensing cost. In this paper we propose CheapUCB, an algorithm that matches the regret guarantees of the known algorithms for this setting and at the same time guarantees a linear cost again over them. As a by-product of our analysis, we establish a Ω(dT) lower bound on the cumulative regret of spectral bandits for a class of graphs with effective dimension d.

Significant work has been recently dedicated to the stochastic delayed bandit setting because of its relevance in applications. The applicability of existing algorithms is however restricted by the fact that strong assumptions are often made on the delay distributions, such as full observability, restrictive shape constraints, or uniformity over arms. In this work, we weaken them significantly and only assume that there is a bound on the tail of the delay. In particular, we cover the important case where the delay distributions vary across arms, and the case where the delays are heavy-tailed. Addressing these difficulties, we propose a simple but efficient UCB-based algorithm called the PatientBandits. We provide both problems-dependent and problems-independent bounds on the regret as well as performance lower bounds.

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

We consider an online learning problem with one-sided feedback, in which the learner is able to observe the true label only for positively predicted instances. On each round, k instances arrive and receive classification outcomes according to a randomized policy deployed by the learner, whose goal is to maximize accuracy while deploying individually fair policies. We first extend the framework of Bechavod et al. (2020), which relies on the existence of a human fairness auditor for detecting fairness violations, to instead incorporate feedback from dynamically-selected panels of multiple, possibly inconsistent, auditors. We then construct an efficient reduction from our problem of online learning with one-sided feedback and a panel reporting fairness violations to the contextual combinatorial semi-bandit problem (Cesa-Bianchi & Lugosi, 2009, Gy\"{o}rgy et al., 2007). Finally, we show how to leverage the guarantees of two algorithms in the contextual combinatorial semi-bandit setting: Exp2 (Bubeck et al., 2012) and the oracle-efficient Context-Semi-Bandit-FTPL (Syrgkanis et al., 2016), to provide multi-criteria no regret guarantees simultaneously for accuracy and fairness. Our results eliminate two potential sources of bias from prior work: the "hidden outcomes" that are not available to an algorithm operating in the full information setting, and human biases that might be present in any single human auditor, but can be mitigated by selecting a well chosen panel.

In this paper, we introduce Randomized Q-learning (RandQL), a novel randomized model-free algorithm for regret minimization in episodic Markov Decision Processes (MDPs). To the best of our knowledge, RandQL is the first tractable model-free posterior sampling-based algorithm. We analyze the performance of RandQL in both tabular and non-tabular metric space settings. In tabular MDPs, RandQL achieves a regret bound of order O(H^{5SAT}), where H is the planning horizon, S is the number of states, A is the number of actions, and T is the number of episodes. For a metric state-action space, RandQL enjoys a regret bound of order O(H^{5/2} T^{(d_z+1)/(d_z+2)}), where d_z denotes the zooming dimension. Notably, RandQL achieves optimistic exploration without using bonuses, relying instead on a novel idea of learning rate randomization. Our empirical study shows that RandQL outperforms existing approaches on baseline exploration environments.

This paper investigates the problem of generalized linear bandits with heavy-tailed rewards, whose (1+epsilon)-th moment is bounded for some epsilonin (0,1]. Although there exist methods for generalized linear bandits, most of them focus on bounded or sub-Gaussian rewards and are not well-suited for many real-world scenarios, such as financial markets and web-advertising. To address this issue, we propose two novel algorithms based on truncation and mean of medians. These algorithms achieve an almost optimal regret bound of O(dT^{1{1+epsilon}}), where d is the dimension of contextual information and T is the time horizon. Our truncation-based algorithm supports online learning, distinguishing it from existing truncation-based approaches. Additionally, our mean-of-medians-based algorithm requires only O(log T) rewards and one estimator per epoch, making it more practical. Moreover, our algorithms improve the regret bounds by a logarithmic factor compared to existing algorithms when epsilon=1. Numerical experimental results confirm the merits of our algorithms.

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows us to obtain a Gaussian-like approximation for the sum distribution using geometry and complex analysis methods. Our results generalize similar bounds for the Beta distribution obtained in the seminal paper Alfers and Dinges [1984]. Additionally, our results can be considered a sharp non-asymptotic version of the inverse of Sanov's theorem studied by Ganesh and O'Connell [1999] in the Bayesian setting. Based on these results, we derive new deviation bounds for the Dirichlet process posterior means with application to Bayesian bootstrap. Finally, we apply our estimates to the analysis of the Multinomial Thompson Sampling (TS) algorithm in multi-armed bandits and significantly sharpen the existing regret bounds by making them independent of the size of the arms distribution support.

We consider a stochastic bandit problem with infinitely many arms. In this setting, the learner has no chance of trying all the arms even once and has to dedicate its limited number of samples only to a certain number of arms. All previous algorithms for this setting were designed for minimizing the cumulative regret of the learner. In this paper, we propose an algorithm aiming at minimizing the simple regret. As in the cumulative regret setting of infinitely many armed bandits, the rate of the simple regret will depend on a parameter β characterizing the distribution of the near-optimal arms. We prove that depending on β, our algorithm is minimax optimal either up to a multiplicative constant or up to a log(n) factor. We also provide extensions to several important cases: when β is unknown, in a natural setting where the near-optimal arms have a small variance, and in the case of unknown time horizon.

We study a graph bandit setting where the objective of the learner is to detect the most influential node of a graph by requesting as little information from the graph as possible. One of the relevant applications for this setting is marketing in social networks, where the marketer aims at finding and taking advantage of the most influential customers. The existing approaches for bandit problems on graphs require either partial or complete knowledge of the graph. In this paper, we do not assume any knowledge of the graph, but we consider a setting where it can be gradually discovered in a sequential and active way. At each round, the learner chooses a node of the graph and the only information it receives is a stochastic set of the nodes that the chosen node is currently influencing. To address this setting, we propose BARE, a bandit strategy for which we prove a regret guarantee that scales with the detectable dimension, a problem dependent quantity that is often much smaller than the number of nodes.

We consider a resource-aware variant of the classical multi-armed bandit problem: In each round, the learner selects an arm and determines a resource limit. It then observes a corresponding (random) reward, provided the (random) amount of consumed resources remains below the limit. Otherwise, the observation is censored, i.e., no reward is obtained. For this problem setting, we introduce a measure of regret, which incorporates the actual amount of allocated resources of each learning round as well as the optimality of realizable rewards. Thus, to minimize regret, the learner needs to set a resource limit and choose an arm in such a way that the chance to realize a high reward within the predefined resource limit is high, while the resource limit itself should be kept as low as possible. We propose a UCB-inspired online learning algorithm, which we analyze theoretically in terms of its regret upper bound. In a simulation study, we show that our learning algorithm outperforms straightforward extensions of standard multi-armed bandit algorithms.

Thompson Sampling (TS) has attracted a lot of interest due to its good empirical performance, in particular in the computational advertising. Though successful, the tools for its performance analysis appeared only recently. In this paper, we describe and analyze SpectralTS algorithm for a bandit problem, where the payoffs of the choices are smooth given an underlying graph. In this setting, each choice is a node of a graph and the expected payoffs of the neighboring nodes are assumed to be similar. Although the setting has application both in recommender systems and advertising, the traditional algorithms would scale poorly with the number of choices. For that purpose we consider an effective dimension d, which is small in real-world graphs. We deliver the analysis showing that the regret of SpectralTS scales as d*sqrt(T ln N) with high probability, where T is the time horizon and N is the number of choices. Since a d*sqrt(T ln N) regret is comparable to the known results, SpectralTS offers a computationally more efficient alternative. We also show that our algorithm is competitive on both synthetic and real-world data.

A commonly used heuristic in RL is experience replay (e.g.~lin1993reinforcement, mnih2015human), in which a learner stores and re-uses past trajectories as if they were sampled online. In this work, we initiate a rigorous study of this heuristic in the setting of tabular Q-learning. We provide a convergence rate guarantee, and discuss how it compares to the convergence of Q-learning depending on important parameters such as the frequency and number of replay iterations. We also provide theoretical evidence showing when we might expect this heuristic to strictly improve performance, by introducing and analyzing a simple class of MDPs. Finally, we provide some experiments to support our theoretical findings.

POMDPs capture a broad class of decision making problems, but hardness results suggest that learning is intractable even in simple settings due to the inherent partial observability. However, in many realistic problems, more information is either revealed or can be computed during some point of the learning process. Motivated by diverse applications ranging from robotics to data center scheduling, we formulate a Hindsight Observable Markov Decision Process (HOMDP) as a POMDP where the latent states are revealed to the learner in hindsight and only during training. We introduce new algorithms for the tabular and function approximation settings that are provably sample-efficient with hindsight observability, even in POMDPs that would otherwise be statistically intractable. We give a lower bound showing that the tabular algorithm is optimal in its dependence on latent state and observation cardinalities.

Learning with few labeled tabular samples is often an essential requirement for industrial machine learning applications as varieties of tabular data suffer from high annotation costs or have difficulties in collecting new samples for novel tasks. Despite the utter importance, such a problem is quite under-explored in the field of tabular learning, and existing few-shot learning schemes from other domains are not straightforward to apply, mainly due to the heterogeneous characteristics of tabular data. In this paper, we propose a simple yet effective framework for few-shot semi-supervised tabular learning, coined Self-generated Tasks from UNlabeled Tables (STUNT). Our key idea is to self-generate diverse few-shot tasks by treating randomly chosen columns as a target label. We then employ a meta-learning scheme to learn generalizable knowledge with the constructed tasks. Moreover, we introduce an unsupervised validation scheme for hyperparameter search (and early stopping) by generating a pseudo-validation set using STUNT from unlabeled data. Our experimental results demonstrate that our simple framework brings significant performance gain under various tabular few-shot learning benchmarks, compared to prior semi- and self-supervised baselines. Code is available at https://github.com/jaehyun513/STUNT.

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each recommended item is a node and its expected rating is similar to its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose two algorithms for solving our problem that scale linearly in this dimension. Our experiments on real-world content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens nodes evaluations.

Multi-vector late-interaction retrievers such as ColBERT achieve state-of-the-art retrieval quality, but their query-time cost is dominated by exhaustively computing token-level MaxSim interactions for every candidate document. While approximating late interaction with single-vector representations reduces cost, it often incurs substantial accuracy loss. We introduce Col-Bandit, a query-time pruning algorithm that reduces this computational burden by casting reranking as a finite-population Top-K identification problem. Col-Bandit maintains uncertainty-aware bounds over partially observed document scores and adaptively reveals only the (document, query token) MaxSim entries needed to determine the top results under statistical decision bounds with a tunable relaxation. Unlike coarse-grained approaches that prune entire documents or tokens offline, Col-Bandit sparsifies the interaction matrix on the fly. It operates as a zero-shot, drop-in layer over standard multi-vector systems, requiring no index modifications, offline preprocessing, or model retraining. Experiments on textual (BEIR) and multimodal (REAL-MM-RAG) benchmarks show that Col-Bandit preserves ranking fidelity while reducing MaxSim FLOPs by up to 5times, indicating that dense late-interaction scoring contains substantial redundancy that can be identified and pruned efficiently at query time.

We consider a contextual combinatorial bandit problem where in each round a learning agent selects a subset of arms and receives feedback on the selected arms according to their scores. The score of an arm is an unknown function of the arm's feature. Approximating this unknown score function with deep neural networks, we propose algorithms: Combinatorial Neural UCB (CN-UCB) and Combinatorial Neural Thompson Sampling (CN-TS). We prove that CN-UCB achieves mathcal{O}(d T) or mathcal{O}(tilde{d T K}) regret, where d is the effective dimension of a neural tangent kernel matrix, K is the size of a subset of arms, and T is the time horizon. For CN-TS, we adapt an optimistic sampling technique to ensure the optimism of the sampled combinatorial action, achieving a worst-case (frequentist) regret of mathcal{O}(d TK). To the best of our knowledge, these are the first combinatorial neural bandit algorithms with regret performance guarantees. In particular, CN-TS is the first Thompson sampling algorithm with the worst-case regret guarantees for the general contextual combinatorial bandit problem. The numerical experiments demonstrate the superior performances of our proposed algorithms.

We study the problem of learning a Nash equilibrium (NE) in an imperfect information game (IIG) through self-play. Precisely, we focus on two-player, zero-sum, episodic, tabular IIG under the perfect-recall assumption where the only feedback is realizations of the game (bandit feedback). In particular, the dynamic of the IIG is not known -- we can only access it by sampling or interacting with a game simulator. For this learning setting, we provide the Implicit Exploration Online Mirror Descent (IXOMD) algorithm. It is a model-free algorithm with a high-probability bound on the convergence rate to the NE of order 1/T where T is the number of played games. Moreover, IXOMD is computationally efficient as it needs to perform the updates only along the sampled trajectory.

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each item we can recommend is a node and its expected rating is similar to its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret with respect to the optimal policy would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose two algorithms for solving our problem that scale linearly and sublinearly in this dimension. Our experiments on real-world content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens of nodes evaluations.

We consider the regret minimization task in a dueling bandits problem with context information. In every round of the sequential decision problem, the learner makes a context-dependent selection of two choice alternatives (arms) to be compared with each other and receives feedback in the form of noisy preference information. We assume that the feedback process is determined by a linear stochastic transitivity model with contextualized utilities (CoLST), and the learner's task is to include the best arm (with highest latent context-dependent utility) in the duel. We propose a computationally efficient algorithm, CoLSTIM, which makes its choice based on imitating the feedback process using perturbed context-dependent utility estimates of the underlying CoLST model. If each arm is associated with a d-dimensional feature vector, we show that CoLSTIM achieves a regret of order tilde O( dT) after T learning rounds. Additionally, we also establish the optimality of CoLSTIM by showing a lower bound for the weak regret that refines the existing average regret analysis. Our experiments demonstrate its superiority over state-of-art algorithms for special cases of CoLST models.

We investigate stochastic combinatorial multi-armed bandit with semi-bandit feedback (CMAB). In CMAB, the question of the existence of an efficient policy with an optimal asymptotic regret (up to a factor poly-logarithmic with the action size) is still open for many families of distributions, including mutually independent outcomes, and more generally the multivariate sub-Gaussian family. We propose to answer the above question for these two families by analyzing variants of the Combinatorial Thompson Sampling policy (CTS). For mutually independent outcomes in [0,1], we propose a tight analysis of CTS using Beta priors. We then look at the more general setting of multivariate sub-Gaussian outcomes and propose a tight analysis of CTS using Gaussian priors. This last result gives us an alternative to the Efficient Sampling for Combinatorial Bandit policy (ESCB), which, although optimal, is not computationally efficient.

We study decision making in environments where the reward is only partially observed, but can be modeled as a function of an action and an observed context. This setting, known as contextual bandits, encompasses a wide variety of applications including health-care policy and Internet advertising. A central task is evaluation of a new policy given historic data consisting of contexts, actions and received rewards. The key challenge is that the past data typically does not faithfully represent proportions of actions taken by a new policy. Previous approaches rely either on models of rewards or models of the past policy. The former are plagued by a large bias whereas the latter have a large variance. In this work, we leverage the strength and overcome the weaknesses of the two approaches by applying the doubly robust technique to the problems of policy evaluation and optimization. We prove that this approach yields accurate value estimates when we have either a good (but not necessarily consistent) model of rewards or a good (but not necessarily consistent) model of past policy. Extensive empirical comparison demonstrates that the doubly robust approach uniformly improves over existing techniques, achieving both lower variance in value estimation and better policies. As such, we expect the doubly robust approach to become common practice.

The study of collaborative multi-agent bandits has attracted significant attention recently. In light of this, we initiate the study of a new collaborative setting, consisting of N agents such that each agent is learning one of M stochastic multi-armed bandits to minimize their group cumulative regret. We develop decentralized algorithms which facilitate collaboration between the agents under two scenarios. We characterize the performance of these algorithms by deriving the per agent cumulative regret and group regret upper bounds. We also prove lower bounds for the group regret in this setting, which demonstrates the near-optimal behavior of the proposed algorithms.

We study linear contextual bandits in the misspecified setting, where the expected reward function can be approximated by a linear function class up to a bounded misspecification level zeta>0. We propose an algorithm based on a novel data selection scheme, which only selects the contextual vectors with large uncertainty for online regression. We show that, when the misspecification level zeta is dominated by tilde O (Delta / d) with Delta being the minimal sub-optimality gap and d being the dimension of the contextual vectors, our algorithm enjoys the same gap-dependent regret bound tilde O (d^2/Delta) as in the well-specified setting up to logarithmic factors. In addition, we show that an existing algorithm SupLinUCB (Chu et al., 2011) can also achieve a gap-dependent constant regret bound without the knowledge of sub-optimality gap Delta. Together with a lower bound adapted from Lattimore et al. (2020), our result suggests an interplay between misspecification level and the sub-optimality gap: (1) the linear contextual bandit model is efficiently learnable when zeta leq tilde O(Delta / d); and (2) it is not efficiently learnable when zeta geq tilde Omega({Delta} / {d}). Experiments on both synthetic and real-world datasets corroborate our theoretical results.

We study the non-stationary dueling bandits problem with K arms, where the time horizon T consists of M stationary segments, each of which is associated with its own preference matrix. The learner repeatedly selects a pair of arms and observes a binary preference between them as feedback. To minimize the accumulated regret, the learner needs to pick the Condorcet winner of each stationary segment as often as possible, despite preference matrices and segment lengths being unknown. We propose the Beat, the, Winner, Reset algorithm and prove a bound on its expected binary weak regret in the stationary case, which tightens the bound of current state-of-art algorithms. We also show a regret bound for the non-stationary case, without requiring knowledge of M or T. We further propose and analyze two meta-algorithms, DETECT for weak regret and Monitored, Dueling, Bandits for strong regret, both based on a detection-window approach that can incorporate any dueling bandit algorithm as a black-box algorithm. Finally, we prove a worst-case lower bound for expected weak regret in the non-stationary case.

Bandits with preference feedback present a powerful tool for optimizing unknown target functions when only pairwise comparisons are allowed instead of direct value queries. This model allows for incorporating human feedback into online inference and optimization and has been employed in systems for fine-tuning large language models. The problem is well understood in simplified settings with linear target functions or over finite small domains that limit practical interest. Taking the next step, we consider infinite domains and nonlinear (kernelized) rewards. In this setting, selecting a pair of actions is quite challenging and requires balancing exploration and exploitation at two levels: within the pair, and along the iterations of the algorithm. We propose MAXMINLCB, which emulates this trade-off as a zero-sum Stackelberg game, and chooses action pairs that are informative and yield favorable rewards. MAXMINLCB consistently outperforms existing algorithms and satisfies an anytime-valid rate-optimal regret guarantee. This is due to our novel preference-based confidence sequences for kernelized logistic estimators.

Simple regret is a natural and parameter-free performance criterion for pure exploration in multi-armed bandits yet is less popular than the probability of missing the best arm or an epsilon-good arm, perhaps due to lack of easy ways to characterize it. In this paper, we make significant progress on minimizing simple regret in both data-rich (Tge n) and data-poor regime (T le n) where n is the number of arms, and T is the number of samples. At its heart is our improved instance-dependent analysis of the well-known Sequential Halving (SH) algorithm, where we bound the probability of returning an arm whose mean reward is not within epsilon from the best (i.e., not epsilon-good) for any choice of epsilon>0, although epsilon is not an input to SH. Our bound not only leads to an optimal worst-case simple regret bound of n/T up to logarithmic factors but also essentially matches the instance-dependent lower bound for returning an epsilon-good arm reported by Katz-Samuels and Jamieson (2020). For the more challenging data-poor regime, we propose Bracketing SH (BSH) that enjoys the same improvement even without sampling each arm at least once. Our empirical study shows that BSH outperforms existing methods on real-world tasks.

We study linear dueling bandits in volatile environments characterized by the simultaneous presence of post-serving contexts, delayed feedback, and adversarial corruption. Feedback is subject to unknown stochastic or adversarial delays and a cumulative corruption budget C. To address these challenges, we propose e RCDP-UCB, which integrates a learned approximator that predicts post-serving contexts from pre-serving information. It further employs an adaptive weighting strategy that clips feature vectors to mitigate the impact of corrupted and delayed observations simultaneously. Under standard regularity conditions and a parametric post-serving mapping, we rigorously establish that our algorithm is delay-regime-agnostic, achieving a regret upper bound of mathcal{O}(d(T + C + D)), where d is the total feature dimension and D encapsulates the delay complexity. Crucially, our analysis reveals an additive cost structure between corruption and delay, avoiding the multiplicative degradation typical of prior works. We further establish lower bounds that nearly match our upper bounds up to a d factor for adversarial delays in the absence of post-serving contexts. Code is available at https://github.com/youngmin0oh/rcdp-public.

The Multi-armed bandit offer the advantage to learn and exploit the already learnt knowledge at the same time. This capability allows this approach to be applied in different domains, going from clinical trials where the goal is investigating the effects of different experimental treatments while minimizing patient losses, to adaptive routing where the goal is to minimize the delays in a network. This article provides a review of the recent results on applying bandit to real-life scenario and summarize the state of the art for each of these fields. Different techniques has been proposed to solve this problem setting, like epsilon-greedy, Upper confident bound (UCB) and Thompson Sampling (TS). We are showing here how this algorithms were adapted to solve the different problems of exploration exploitation.

Policy optimization methods are popular reinforcement learning algorithms in practice. Recent works have built theoretical foundation for them by proving T regret bounds even when the losses are adversarial. Such bounds are tight in the worst case but often overly pessimistic. In this work, we show that in tabular Markov decision processes (MDPs), by properly designing the regularizer, the exploration bonus and the learning rates, one can achieve a more favorable polylog(T) regret when the losses are stochastic, without sacrificing the worst-case guarantee in the adversarial regime. To our knowledge, this is also the first time a gap-dependent polylog(T) regret bound is shown for policy optimization. Specifically, we achieve this by leveraging a Tsallis entropy or a Shannon entropy regularizer in the policy update. Then we show that under known transitions, we can further obtain a first-order regret bound in the adversarial regime by leveraging the log-barrier regularizer.

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this work, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each item we can recommend is a node of an undirected graph and its expected rating is similar to the one of its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret with respect to the optimal policy would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose three algorithms for solving our problem that scale linearly and sublinearly in this dimension. Our experiments on content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens of node evaluations.

In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward g(gamma, v) depends on the proposed threshold gamma and latent value v and it can be only achieved if the threshold is lower than or equal to the unknown latent value. This problem has broad applications in practical scenarios, e.g., reserve price optimization in online auctions, online task assignments in crowdsourcing, setting recruiting bars in hiring, etc. We first characterize the query complexity of learning a threshold with the expected reward at most epsilon smaller than the optimum and prove that the number of queries needed can be infinitely large even when g(gamma, v) is monotone with respect to both gamma and v. On the positive side, we provide a tight query complexity Theta(1/epsilon^3) when g is monotone and the CDF of value distribution is Lipschitz. Moreover, we show a tight Theta(1/epsilon^3) query complexity can be achieved as long as g satisfies one-sided Lipschitzness, which provides a complete characterization for this problem. Finally, we extend this model to an online learning setting and demonstrate a tight Theta(T^{2/3}) regret bound using continuous-arm bandit techniques and the aforementioned query complexity results.

Regret minimization in streaming multi-armed bandits (MABs) has been studied extensively in recent years. In the single-pass setting with K arms and T trials, a regret lower bound of Omega(T^{2/3}) has been proved for any algorithm with o(K) memory (Maiti et al. [NeurIPS'21]; Agarwal at al. [COLT'22]). On the other hand, however, the previous best regret upper bound is still O(K^{1/3} T^{2/3}log^{1/3}(T)), which is achieved by the streaming implementation of the simple uniform exploration. The O(K^{1/3}log^{1/3}(T)) gap leaves the open question of the tight regret bound in the single-pass MABs with sublinear arm memory. In this paper, we answer this open problem and complete the picture of regret minimization in single-pass streaming MABs. We first improve the regret lower bound to Omega(K^{1/3}T^{2/3}) for algorithms with o(K) memory, which matches the uniform exploration regret up to a logarithm factor in T. We then show that the log^{1/3}(T) factor is not necessary, and we can achieve O(K^{1/3}T^{2/3}) regret by finding an varepsilon-best arm and committing to it in the rest of the trials. For regret minimization with high constant probability, we can apply the single-memory varepsilon-best arm algorithms in Jin et al. [ICML'21] to obtain the optimal bound. Furthermore, for the expected regret minimization, we design an algorithm with a single-arm memory that achieves O(K^{1/3} T^{2/3}log(K)) regret, and an algorithm with O(log^{*}(n))-memory with the optimal O(K^{1/3} T^{2/3}) regret following the varepsilon-best arm algorithm in Assadi and Wang [STOC'20]. We further tested the empirical performances of our algorithms. The simulation results show that the proposed algorithms consistently outperform the benchmark uniform exploration algorithm by a large margin, and on occasion, reduce the regret by up to 70%.

Reinforcement Learning from Human Feedback (RLHF) has become a popular approach to align language models (LMs) with human preferences. This method involves collecting a large dataset of human pairwise preferences across various text generations and using it to infer (implicitly or explicitly) a reward model. Numerous methods have been proposed to learn the reward model and align a LM with it. However, the costly process of collecting human preferences has received little attention and could benefit from theoretical insights. This paper addresses this issue and aims to formalize the reward training model in RLHF. We frame the selection of an effective dataset as a simple regret minimization task, using a linear contextual dueling bandit method. Given the potentially large number of arms, this approach is more coherent than the best-arm identification setting. We then propose an offline framework for solving this problem. Under appropriate assumptions - linearity of the reward model in the embedding space, and boundedness of the reward parameter - we derive bounds on the simple regret. Finally, we provide a lower bound that matches our upper bound up to constant and logarithmic terms. To our knowledge, this is the first theoretical contribution in this area to provide an offline approach as well as worst-case guarantees.

The rapid advancement in large language models (LLMs) has brought forth a diverse range of models with varying capabilities that excel in different tasks and domains. However, selecting the optimal LLM for user queries often involves a challenging trade-off between accuracy and cost, a problem exacerbated by the diverse demands of individual queries. In this work, we present a novel framework that formulates the LLM selection process as a multi-armed bandit problem, enabling dynamic and intelligent routing of queries to the most appropriate model. Our approach incorporates a preference-conditioned dynamic routing mechanism, allowing users to specify their preferences at inference time, thereby offering a customizable balance between performance and cost. Additionally, our selection policy is designed to generalize to unseen LLMs, ensuring adaptability to new models as they emerge. Experimental results demonstrate that our method achieves significant improvements in both accuracy and cost-effectiveness across various LLM platforms, showcasing the potential of our framework to adaptively optimize LLM selection in real-world scenarios.

Tabular data serves as the backbone of modern data analysis and scientific research. While Large Language Models (LLMs) fine-tuned via Supervised Fine-Tuning (SFT) have significantly improved natural language interaction with such structured data, they often fall short in handling the complex, multi-step reasoning and robust code execution required for real-world table tasks. Reinforcement Learning (RL) offers a promising avenue to enhance these capabilities, yet its application in the tabular domain faces three critical hurdles: the scarcity of high-quality agentic trajectories with closed-loop code execution and environment feedback on diverse table structures, the extreme heterogeneity of feedback signals ranging from rigid SQL execution to open-ended data interpretation, and the risk of catastrophic forgetting of general knowledge during vertical specialization. To overcome these challenges and unlock advanced reasoning on complex tables, we introduce TableGPT-R1, a specialized tabular model built on a systematic RL framework. Our approach integrates a comprehensive data engineering pipeline that synthesizes difficulty-stratified agentic trajectories for both supervised alignment and RL rollouts, a task-adaptive reward system that combines rule-based verification with a criteria-injected reward model and incorporates process-level step reward shaping with behavioral regularization, and a multi-stage training framework that progressively stabilizes reasoning before specializing in table-specific tasks. Extensive evaluations demonstrate that TableGPT-R1 achieves state-of-the-art performance on authoritative benchmarks, significantly outperforming baseline models while retaining robust general capabilities. Our model is available at https://huggingface.co/tablegpt/TableGPT-R1.

We study the problem of designing mechanisms for information acquisition scenarios. This setting models strategic interactions between an uniformed receiver and a set of informed senders. In our model the senders receive information about the underlying state of nature and communicate their observation (either truthfully or not) to the receiver, which, based on this information, selects an action. Our goal is to design mechanisms maximizing the receiver's utility while incentivizing the senders to report truthfully their information. First, we provide an algorithm that efficiently computes an optimal incentive compatible (IC) mechanism. Then, we focus on the online problem in which the receiver sequentially interacts in an unknown game, with the objective of minimizing the cumulative regret w.r.t. the optimal IC mechanism, and the cumulative violation of the incentive compatibility constraints. We investigate two different online scenarios, i.e., the full and bandit feedback settings. For the full feedback problem, we propose an algorithm that guarantees mathcal O(sqrt T) regret and violation, while for the bandit feedback setting we present an algorithm that attains mathcal O(T^{alpha}) regret and mathcal O(T^{1-alpha/2}) violation for any alphain[1/2, 1]. Finally, we complement our results providing a tight lower bound.

As predictive models are increasingly deployed in high-stakes settings such as credit approval, there is a growing need for post-hoc methods that provide recourse to affected individuals. Many such models operate on tabular data, where features correspond to real-world attributes. Recently, in-context learning (ICL) has enabled large language models to perform tabular prediction by conditioning on labeled examples at inference time, without explicit training. However, algorithmic recourse for tabular decision-making under ICL remains largely unexplored. In this work, we present the first study of algorithmic recourse for tabular data under ICL. We carry out a theoretical analysis, showing that recourse remains well-defined and bounded, and we characterize how recourse converges toward classical solutions as the context size increases. In practice, we propose a novel zeroth-order recourse framework, Adaptive Subspace Recourse for In-Context Learning (ASR-ICL), that efficiently generates actionable and sparse recourse for black-box ICL models. The proposed framework naturally extends to multi-class tabular tasks. Experiments across multiple real-world datasets and models demonstrate that ASR-ICL achieves recourse quality comparable to existing methods with fewer queries and empirically confirm the predicted convergence behavior, supporting our theoretical analysis.

In this paper we propose two algorithms in the tabular setting and an algorithm for the function approximation setting for the Stochastic Shortest Path (SSP) problem. SSP problems form an important class of problems in Reinforcement Learning (RL), as other types of cost-criteria in RL can be formulated in the setting of SSP. We show asymptotic almost-sure convergence for all our algorithms. We observe superior performance of our tabular algorithms compared to other well-known convergent RL algorithms. We further observe reliable performance of our function approximation algorithm compared to other algorithms in the function approximation setting.

We investigate an active pure-exploration setting, that includes best-arm identification, in the context of linear stochastic bandits. While asymptotically optimal algorithms exist for standard multi-arm bandits, the existence of such algorithms for the best-arm identification in linear bandits has been elusive despite several attempts to address it. First, we provide a thorough comparison and new insight over different notions of optimality in the linear case, including G-optimality, transductive optimality from optimal experimental design and asymptotic optimality. Second, we design the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits. As a consequence, our algorithm naturally bypasses the pitfall caused by a simple but difficult instance, that most prior algorithms had to be engineered to deal with explicitly. Finally, we avoid the need to fully solve an optimal design problem by providing an approach that entails an efficient implementation.

Large Language Models (LLMs) have revolutionized natural language processing, but their varying capabilities and costs pose challenges in practical applications. LLM routing addresses this by dynamically selecting the most suitable LLM for each query/task. Previous approaches treat this as a supervised learning problem, assuming complete knowledge of optimal query-LLM pairings. However, real-world scenarios lack such comprehensive mappings and face evolving user queries. We thus propose to study LLM routing as a contextual bandit problem, enabling adaptive decision-making using bandit feedback without requiring exhaustive inference across all LLMs for all queries (in contrast to supervised routing). To address this problem, we develop a shared embedding space for queries and LLMs, where query and LLM embeddings are aligned to reflect their affinity. This space is initially learned from offline human preference data and refined through online bandit feedback. We instantiate this idea through Preference-prior Informed Linucb fOr adaptive rouTing (PILOT), a novel extension of LinUCB. To handle diverse user budgets for model routing, we introduce an online cost policy modeled as a multi-choice knapsack problem, ensuring resource-efficient routing.

Policy Optimization (PO) is one of the most popular methods in Reinforcement Learning (RL). Thus, theoretical guarantees for PO algorithms have become especially important to the RL community. In this paper, we study PO in adversarial MDPs with a challenge that arises in almost every real-world application -- delayed bandit feedback. We give the first near-optimal regret bounds for PO in tabular MDPs, and may even surpass state-of-the-art (which uses less efficient methods). Our novel Delay-Adapted PO (DAPO) is easy to implement and to generalize, allowing us to extend our algorithm to: (i) infinite state space under the assumption of linear Q-function, proving the first regret bounds for delayed feedback with function approximation. (ii) deep RL, demonstrating its effectiveness in experiments on MuJoCo domains.

The best neural architecture for a given machine learning problem depends on many factors: not only the complexity and structure of the dataset, but also on resource constraints including latency, compute, energy consumption, etc. Neural architecture search (NAS) for tabular datasets is an important but under-explored problem. Previous NAS algorithms designed for image search spaces incorporate resource constraints directly into the reinforcement learning (RL) rewards. However, for NAS on tabular datasets, this protocol often discovers suboptimal architectures. This paper develops TabNAS, a new and more effective approach to handle resource constraints in tabular NAS using an RL controller motivated by the idea of rejection sampling. TabNAS immediately discards any architecture that violates the resource constraints without training or learning from that architecture. TabNAS uses a Monte-Carlo-based correction to the RL policy gradient update to account for this extra filtering step. Results on several tabular datasets demonstrate the superiority of TabNAS over previous reward-shaping methods: it finds better models that obey the constraints.

These lecture notes give a statistical perspective on the foundations of reinforcement learning and interactive decision making. We present a unifying framework for addressing the exploration-exploitation dilemma using frequentist and Bayesian approaches, with connections and parallels between supervised learning/estimation and decision making as an overarching theme. Special attention is paid to function approximation and flexible model classes such as neural networks. Topics covered include multi-armed and contextual bandits, structured bandits, and reinforcement learning with high-dimensional feedback.

We study distributed contextual linear bandits with stochastic contexts, where N agents act cooperatively to solve a linear bandit-optimization problem with d-dimensional features over the course of T rounds. For this problem, we derive the first ever information-theoretic lower bound Omega(dN) on the communication cost of any algorithm that performs optimally in a regret minimization setup. We then propose a distributed batch elimination version of the LinUCB algorithm, DisBE-LUCB, where the agents share information among each other through a central server. We prove that the communication cost of DisBE-LUCB matches our lower bound up to logarithmic factors. In particular, for scenarios with known context distribution, the communication cost of DisBE-LUCB is only mathcal{O}(dN) and its regret is {mathcal{O}}(dNT), which is of the same order as that incurred by an optimal single-agent algorithm for NT rounds. We also provide similar bounds for practical settings where the context distribution can only be estimated. Therefore, our proposed algorithm is nearly minimax optimal in terms of both regret and communication cost. Finally, we propose DecBE-LUCB, a fully decentralized version of DisBE-LUCB, which operates without a central server, where agents share information with their immediate neighbors through a carefully designed consensus procedure.

Contextual bandits are a rich model for sequential decision making given side information, with important applications, e.g., in recommender systems. We propose novel algorithms for contextual bandits harnessing neural networks to approximate the unknown reward function. We resolve the open problem of proving sublinear regret bounds in this setting for general context sequences, considering both fully-connected and convolutional networks. To this end, we first analyze NTK-UCB, a kernelized bandit optimization algorithm employing the Neural Tangent Kernel (NTK), and bound its regret in terms of the NTK maximum information gain gamma_T, a complexity parameter capturing the difficulty of learning. Our bounds on gamma_T for the NTK may be of independent interest. We then introduce our neural network based algorithm NN-UCB, and show that its regret closely tracks that of NTK-UCB. Under broad non-parametric assumptions about the reward function, our approach converges to the optimal policy at a mathcal{O}(T^{-1/2d}) rate, where d is the dimension of the context.

LLM-as-a-judge has emerged as a cornerstone technique for evaluating large language models by leveraging LLM reasoning to score prompt-response pairs. Since LLM judgments are stochastic, practitioners commonly query each pair multiple times to estimate mean scores accurately. This raises a critical challenge: given a fixed computational budget B, how to optimally allocate queries across K prompt-response pairs to minimize estimation error? % We present a principled variance-adaptive approach leveraging multi-armed bandit theory and concentration inequalities. Our method dynamically allocates queries based on estimated score variances, concentrating resources where uncertainty is highest. Further, our algorithm is shown to achieve a worst-case score-estimation error of Oleft(frac{sum_{i=1^K σ_i^2}{B}}right), σ_i^2 being the unknown score variance for pair i in [K] with near-optimal budget allocation. % Experiments on Summarize-From-Feedback and HelpSteer2 demonstrate that our method significantly outperforms uniform allocation, reducing worst-case estimation error while maintaining identical budgets. Our work establishes a theoretical foundation for efficient LLM evaluation with practical implications for AI safety, model alignment, and automated assessment at scale.

We investigate stochastic combinatorial semi-bandits, where the entire joint distribution of outcomes impacts the complexity of the problem instance (unlike in the standard bandits). Typical distributions considered depend on specific parameter values, whose prior knowledge is required in theory but quite difficult to estimate in practice; an example is the commonly assumed sub-Gaussian family. We alleviate this issue by instead considering a new general family of sub-exponential distributions, which contains bounded and Gaussian ones. We prove a new lower bound on the expected regret on this family, that is parameterized by the unknown covariance matrix of outcomes, a tighter quantity than the sub-Gaussian matrix. We then construct an algorithm that uses covariance estimates, and provide a tight asymptotic analysis of the regret. Finally, we apply and extend our results to the family of sparse outcomes, which has applications in many recommender systems.

Reinforcement learning from Human Feedback (RLHF) learns from preference signals, while standard Reinforcement Learning (RL) directly learns from reward signals. Preferences arguably contain less information than rewards, which makes preference-based RL seemingly more difficult. This paper theoretically proves that, for a wide range of preference models, we can solve preference-based RL directly using existing algorithms and techniques for reward-based RL, with small or no extra costs. Specifically, (1) for preferences that are drawn from reward-based probabilistic models, we reduce the problem to robust reward-based RL that can tolerate small errors in rewards; (2) for general arbitrary preferences where the objective is to find the von Neumann winner, we reduce the problem to multiagent reward-based RL which finds Nash equilibria for factored Markov games under a restricted set of policies. The latter case can be further reduce to adversarial MDP when preferences only depend on the final state. We instantiate all reward-based RL subroutines by concrete provable algorithms, and apply our theory to a large class of models including tabular MDPs and MDPs with generic function approximation. We further provide guarantees when K-wise comparisons are available.

Large language models (LLMs) currently dominate the field of natural language processing (NLP), representing the state-of-the-art across a diverse array of tasks. Developing a model of this nature, from training to inference, requires making numerous decisions which define a combinatorial search problem. For example, selecting the optimal pre-trained LLM, prompt, or hyperparameters to attain the best performance for a task often requires evaluating multiple candidates on an entire test set. This exhaustive evaluation can be time-consuming and costly, as both inference and metric computation with LLMs are resource-intensive. In this paper, we address the challenge of identifying the best method within a limited budget for evaluating methods on test examples. By leveraging the well-studied multi-armed bandit framework, which sequentially selects the next method-example pair to evaluate, our approach, combining multi-armed bandit algorithms with low-rank factorization, significantly reduces the required resources. Experiments show that our algorithms can identify the top-performing method using only 5-15\% of the typically needed resources, resulting in an 85-95\% reduction in cost.

Contextual multi-armed bandit (MAB) achieves cutting-edge performance on a variety of problems. When it comes to real-world scenarios such as recommendation system and online advertising, however, it is essential to consider the resource consumption of exploration. In practice, there is typically non-zero cost associated with executing a recommendation (arm) in the environment, and hence, the policy should be learned with a fixed exploration cost constraint. It is challenging to learn a global optimal policy directly, since it is a NP-hard problem and significantly complicates the exploration and exploitation trade-off of bandit algorithms. Existing approaches focus on solving the problems by adopting the greedy policy which estimates the expected rewards and costs and uses a greedy selection based on each arm's expected reward/cost ratio using historical observation until the exploration resource is exhausted. However, existing methods are hard to extend to infinite time horizon, since the learning process will be terminated when there is no more resource. In this paper, we propose a hierarchical adaptive contextual bandit method (HATCH) to conduct the policy learning of contextual bandits with a budget constraint. HATCH adopts an adaptive method to allocate the exploration resource based on the remaining resource/time and the estimation of reward distribution among different user contexts. In addition, we utilize full of contextual feature information to find the best personalized recommendation. Finally, in order to prove the theoretical guarantee, we present a regret bound analysis and prove that HATCH achieves a regret bound as low as O(T). The experimental results demonstrate the effectiveness and efficiency of the proposed method on both synthetic data sets and the real-world applications.

Advanced reasoning capabilities in Large Language Models (LLMs) have led to more frequent hallucinations; yet most mitigation work focuses on open-source models for post-hoc detection and parameter editing. The dearth of studies focusing on hallucinations in closed-source models is especially concerning, as they constitute the vast majority of models in institutional deployments. We introduce QueryBandits, a model-agnostic contextual bandit framework that adaptively learns online to select the optimal query-rewrite strategy by leveraging an empirically validated and calibrated reward function. Across 16 QA scenarios, our top QueryBandit (Thompson Sampling) achieves an 87.5% win rate over a No-Rewrite baseline and outperforms zero-shot static policies (e.g., Paraphrase or Expand) by 42.6% and 60.3%, respectively. Moreover, all contextual bandits outperform vanilla bandits across all datasets, with higher feature variance coinciding with greater variance in arm selection. This substantiates our finding that there is no single rewrite policy optimal for all queries. We also discover that certain static policies incur higher cumulative regret than No-Rewrite, indicating that an inflexible query-rewriting policy can worsen hallucinations. Thus, learning an online policy over semantic features with QueryBandits can shift model behavior purely through forward-pass mechanisms, enabling its use with closed-source models and bypassing the need for retraining or gradient-based adaptation.

We study LLM routing, the problem of selecting the best model for each query while balancing user satisfaction, model expertise, and inference cost. We formulate routing as contextual dueling bandits, learning from pairwise preference feedback rather than absolute scores, thereby yielding label-efficient and dynamic adaptation. Building on this formulation, we introduce Category-Calibrated Fine-Tuning (CCFT), a representation-learning method that derives model embeddings from offline data using contrastive fine-tuning with categorical weighting. These embeddings enable the practical instantiation of Feel-Good Thompson Sampling for Contextual Dueling Bandits (FGTS.CDB), a theoretically grounded posterior-sampling algorithm. We propose four variants of the categorical weighting that explicitly integrate model quality and cost, and we empirically evaluate the proposed methods on the RouterBench and MixInstruct datasets. Across both benchmarks, our methods achieve lower cumulative regret and faster convergence, with better robustness and performance-cost balance than strong baselines built with a general-purpose OpenAI embedding model.

Gaussian processes (GP) are a well studied Bayesian approach for the optimization of black-box functions. Despite their effectiveness in simple problems, GP-based algorithms hardly scale to high-dimensional functions, as their per-iteration time and space cost is at least quadratic in the number of dimensions d and iterations t. Given a set of A alternatives to choose from, the overall runtime O(t^3A) is prohibitive. In this paper we introduce BKB (budgeted kernelized bandit), a new approximate GP algorithm for optimization under bandit feedback that achieves near-optimal regret (and hence near-optimal convergence rate) with near-constant per-iteration complexity and remarkably no assumption on the input space or covariance of the GP. We combine a kernelized linear bandit algorithm (GP-UCB) with randomized matrix sketching based on leverage score sampling, and we prove that randomly sampling inducing points based on their posterior variance gives an accurate low-rank approximation of the GP, preserving variance estimates and confidence intervals. As a consequence, BKB does not suffer from variance starvation, an important problem faced by many previous sparse GP approximations. Moreover, we show that our procedure selects at most O(d_{eff}) points, where d_{eff} is the effective dimension of the explored space, which is typically much smaller than both d and t. This greatly reduces the dimensionality of the problem, thus leading to a O(TAd_{eff}^2) runtime and O(A d_{eff}) space complexity.

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical follow-the-regularized-leader (FTRL) algorithm to cope with the label noise. More specifically, for sigma-sub-Gaussian label noise, our analysis provides a regret upper bound of O(sigma^2 d log T) + o(log T), where d is the dimension of the input vector, T is the total number of rounds. We also prove a Omega(sigma^2dlog(T/d)) lower bound for stochastic online linear regression, which indicates that our upper bound is nearly optimal. In addition, we extend our analysis to a more refined Bernstein noise condition. As an application, we study generalized linear bandits with heteroscedastic noise and propose an algorithm based on FTRL to achieve the first variance-aware regret bound.

We propose and deploy an approach to continually train an instruction-following agent from feedback provided by users during collaborative interactions. During interaction, human users instruct an agent using natural language, and provide realtime binary feedback as they observe the agent following their instructions. We design a contextual bandit learning approach, converting user feedback to immediate reward. We evaluate through thousands of human-agent interactions, demonstrating 15.4% absolute improvement in instruction execution accuracy over time. We also show our approach is robust to several design variations, and that the feedback signal is roughly equivalent to the learning signal of supervised demonstration data.

Motivated by the need to efficiently identify multiple candidates in high trial-and-error cost tasks such as drug discovery, we propose a near-optimal algorithm to identify all ε-best arms (i.e., those at most ε worse than the optimum). Specifically, we introduce LinFACT, an algorithm designed to optimize the identification of all ε-best arms in linear bandits. We establish a novel information-theoretic lower bound on the sample complexity of this problem and demonstrate that LinFACT achieves instance optimality by matching this lower bound up to a logarithmic factor. A key ingredient of our proof is to integrate the lower bound directly into the scaling process for upper bound derivation, determining the termination round and thus the sample complexity. We also extend our analysis to settings with model misspecification and generalized linear models. Numerical experiments, including synthetic and real drug discovery data, demonstrate that LinFACT identifies more promising candidates with reduced sample complexity, offering significant computational efficiency and accelerating early-stage exploratory experiments.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

Reinforcement Learning with Verifiable Rewards (RLVR) is an effective paradigm for improving the reasoning capabilities of large language models. However, existing RLVR methods utilize rollouts in an indiscriminate and short-horizon manner: responses of heterogeneous quality within each prompt are treated uniformly, and historical rollouts are discarded after a single use. This leads to noisy supervision, poor sample efficiency, and suboptimal policy updates. We address these issues by formulating rollout scheduling in RLVR as a contextual bandit problem and proposing a unified neural scheduling framework that adaptively selects high-value rollouts throughout training. Each rollout is treated as an arm whose reward is defined by the induced performance gain between consecutive optimization steps. The resulting scheduler supports both noise-aware intra-group selection and adaptive global reuse of historical rollouts within a single principled framework. We provide theoretical justification by deriving sublinear regret bounds and showing that enlarging the rollout buffer improves the achievable performance upper bound. Experiments on six mathematical reasoning benchmarks demonstrate consistent gains in performance and training efficiency across multiple RLVR optimization methods.

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium -- such as Nash equilibrium and (Coarse) Correlated Equilibrium -- from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies' returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed "unilateral concentrability". Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.

Most work on sequential learning assumes a fixed set of actions that are available all the time. However, in practice, actions can consist of picking subsets of readings from sensors that may break from time to time, road segments that can be blocked or goods that are out of stock. In this paper we study learning algorithms that are able to deal with stochastic availability of such unreliable composite actions. We propose and analyze algorithms based on the Follow-The-Perturbed-Leader prediction method for several learning settings differing in the feedback provided to the learner. Our algorithms rely on a novel loss estimation technique that we call Counting Asleep Times. We deliver regret bounds for our algorithms for the previously studied full information and (semi-)bandit settings, as well as a natural middle point between the two that we call the restricted information setting. A special consequence of our results is a significant improvement of the best known performance guarantees achieved by an efficient algorithm for the sleeping bandit problem with stochastic availability. Finally, we evaluate our algorithms empirically and show their improvement over the known approaches.

Despite the recent success of representation learning in sequential decision making, the study of the pure exploration scenario (i.e., identify the best option and minimize the sample complexity) is still limited. In this paper, we study multi-task representation learning for best arm identification in linear bandits (RepBAI-LB) and best policy identification in contextual linear bandits (RepBPI-CLB), two popular pure exploration settings with wide applications, e.g., clinical trials and web content optimization. In these two problems, all tasks share a common low-dimensional linear representation, and our goal is to leverage this feature to accelerate the best arm (policy) identification process for all tasks. For these problems, we design computationally and sample efficient algorithms DouExpDes and C-DouExpDes, which perform double experimental designs to plan optimal sample allocations for learning the global representation. We show that by learning the common representation among tasks, our sample complexity is significantly better than that of the native approach which solves tasks independently. To the best of our knowledge, this is the first work to demonstrate the benefits of representation learning for multi-task pure exploration.

This paper introduces a new principled approach for off-policy learning in contextual bandits. Unlike previous work, our approach does not derive learning principles from intractable or loose bounds. We analyse the problem through the PAC-Bayesian lens, interpreting policies as mixtures of decision rules. This allows us to propose novel generalization bounds and provide tractable algorithms to optimize them. We prove that the derived bounds are tighter than their competitors, and can be optimized directly to confidently improve upon the logging policy offline. Our approach learns policies with guarantees, uses all available data and does not require tuning additional hyperparameters on held-out sets. We demonstrate through extensive experiments the effectiveness of our approach in providing performance guarantees in practical scenarios.

In this paper, we consider the problem of sleeping bandits with stochastic action sets and adversarial rewards. In this setting, in contrast to most work in bandits, the actions may not be available at all times. For instance, some products might be out of stock in item recommendation. The best existing efficient (i.e., polynomial-time) algorithms for this problem only guarantee an O(T^{2/3}) upper-bound on the regret. Yet, inefficient algorithms based on EXP4 can achieve O(T). In this paper, we provide a new computationally efficient algorithm inspired by EXP3 satisfying a regret of order O(T) when the availabilities of each action i in cA are independent. We then study the most general version of the problem where at each round available sets are generated from some unknown arbitrary distribution (i.e., without the independence assumption) and propose an efficient algorithm with O(2^K T) regret guarantee. Our theoretical results are corroborated with experimental evaluations.

We consider the task of identifying the Copeland winner(s) in a dueling bandits problem with ternary feedback. This is an underexplored but practically relevant variant of the conventional dueling bandits problem, in which, in addition to strict preference between two arms, one may observe feedback in the form of an indifference. We provide a lower bound on the sample complexity for any learning algorithm finding the Copeland winner(s) with a fixed error probability. Moreover, we propose POCOWISTA, an algorithm with a sample complexity that almost matches this lower bound, and which shows excellent empirical performance, even for the conventional dueling bandits problem. For the case where the preference probabilities satisfy a specific type of stochastic transitivity, we provide a refined version with an improved worst case sample complexity.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

Reinforcement learning (RL) has increasingly been applied to solve real-world planning problems, with progress in handling large state spaces and time horizons. However, a key bottleneck in many domains is that RL methods cannot accommodate large, combinatorially structured action spaces. In such settings, even representing the set of feasible actions at a single step may require a complex discrete optimization formulation. We leverage recent advances in embedding trained neural networks into optimization problems to propose SEQUOIA, an RL algorithm that directly optimizes for long-term reward over the feasible action space. Our approach embeds a Q-network into a mixed-integer program to select a combinatorial action in each timestep. Here, we focus on planning over restless bandits, a class of planning problems which capture many real-world examples of sequential decision making. We introduce coRMAB, a broader class of restless bandits with combinatorial actions that cannot be decoupled across the arms of the restless bandit, requiring direct solving over the joint, exponentially large action space. We empirically validate SEQUOIA on four novel restless bandit problems with combinatorial constraints: multiple interventions, path constraints, bipartite matching, and capacity constraints. Our approach significantly outperforms existing methods -- which cannot address sequential planning and combinatorial selection simultaneously -- by an average of 24.8\% on these difficult instances.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

We study a new non-stochastic federated multi-armed bandit problem with multiple agents collaborating via a communication network. The losses of the arms are assigned by an oblivious adversary that specifies the loss of each arm not only for each time step but also for each agent, which we call ``doubly adversarial". In this setting, different agents may choose the same arm in the same time step but observe different feedback. The goal of each agent is to find a globally best arm in hindsight that has the lowest cumulative loss averaged over all agents, which necessities the communication among agents. We provide regret lower bounds for any federated bandit algorithm under different settings, when agents have access to full-information feedback, or the bandit feedback. For the bandit feedback setting, we propose a near-optimal federated bandit algorithm called FEDEXP3. Our algorithm gives a positive answer to an open question proposed in Cesa-Bianchi et al. (2016): FEDEXP3 can guarantee a sub-linear regret without exchanging sequences of selected arm identities or loss sequences among agents. We also provide numerical evaluations of our algorithm to validate our theoretical results and demonstrate its effectiveness on synthetic and real-world datasets

In stochastic multi-armed bandits, the reward distribution of each arm is assumed to be stationary. This assumption is often violated in practice (e.g., in recommendation systems), where the reward of an arm may change whenever is selected, i.e., rested bandit setting. In this paper, we consider the non-parametric rotting bandit setting, where rewards can only decrease. We introduce the filtering on expanding window average (FEWA) algorithm that constructs moving averages of increasing windows to identify arms that are more likely to return high rewards when pulled once more. We prove that for an unknown horizon T, and without any knowledge on the decreasing behavior of the K arms, FEWA achieves problem-dependent regret bound of mathcal{O}((KT)), and a problem-independent one of mathcal{O}(KT). Our result substantially improves over the algorithm of Levine et al. (2017), which suffers regret mathcal{O}(K^{1/3}T^{2/3}). FEWA also matches known bounds for the stochastic bandit setting, thus showing that the rotting bandits are not harder. Finally, we report simulations confirming the theoretical improvements of FEWA.

We study learning to learn for the multi-task structured bandit problem where the goal is to learn a near-optimal algorithm that minimizes cumulative regret. The tasks share a common structure and an algorithm should exploit the shared structure to minimize the cumulative regret for an unseen but related test task. We use a transformer as a decision-making algorithm to learn this shared structure from data collected by a demonstrator on a set of training task instances. Our objective is to devise a training procedure such that the transformer will learn to outperform the demonstrator's learning algorithm on unseen test task instances. Prior work on pretraining decision transformers either requires privileged information like access to optimal arms or cannot outperform the demonstrator. Going beyond these approaches, we introduce a pre-training approach that trains a transformer network to learn a near-optimal policy in-context. This approach leverages the shared structure across tasks, does not require access to optimal actions, and can outperform the demonstrator. We validate these claims over a wide variety of structured bandit problems to show that our proposed solution is general and can quickly identify expected rewards on unseen test tasks to support effective exploration.

In the stochastic multi-armed bandit problem, a randomized probability matching policy called Thompson sampling (TS) has shown excellent performance in various reward models. In addition to the empirical performance, TS has been shown to achieve asymptotic problem-dependent lower bounds in several models. However, its optimality has been mainly addressed under light-tailed or one-parameter models that belong to exponential families. In this paper, we consider the optimality of TS for the Pareto model that has a heavy tail and is parameterized by two unknown parameters. Specifically, we discuss the optimality of TS with probability matching priors that include the Jeffreys prior and the reference priors. We first prove that TS with certain probability matching priors can achieve the optimal regret bound. Then, we show the suboptimality of TS with other priors, including the Jeffreys and the reference priors. Nevertheless, we find that TS with the Jeffreys and reference priors can achieve the asymptotic lower bound if one uses a truncation procedure. These results suggest carefully choosing noninformative priors to avoid suboptimality and show the effectiveness of truncation procedures in TS-based policies.

We consider distributed linear bandits where M agents learn collaboratively to minimize the overall cumulative regret incurred by all agents. Information exchange is facilitated by a central server, and both the uplink and downlink communications are carried over channels with fixed capacity, which limits the amount of information that can be transmitted in each use of the channels. We investigate the regret-communication trade-off by (i) establishing information-theoretic lower bounds on the required communications (in terms of bits) for achieving a sublinear regret order; (ii) developing an efficient algorithm that achieves the minimum sublinear regret order offered by centralized learning using the minimum order of communications dictated by the information-theoretic lower bounds. For sparse linear bandits, we show a variant of the proposed algorithm offers better regret-communication trade-off by leveraging the sparsity of the problem.

Motivated by emerging applications such as live-streaming e-commerce, promotions and recommendations, we introduce and solve a general class of non-stationary multi-armed bandit problems that have the following two features: (i) the decision maker can pull and collect rewards from up to K,(ge 1) out of N different arms in each time period; (ii) the expected reward of an arm immediately drops after it is pulled, and then non-parametrically recovers as the arm's idle time increases. With the objective of maximizing the expected cumulative reward over T time periods, we design a class of ``Purely Periodic Policies'' that jointly set a period to pull each arm. For the proposed policies, we prove performance guarantees for both the offline problem and the online problems. For the offline problem when all model parameters are known, the proposed periodic policy obtains an approximation ratio that is at the order of 1-mathcal O(1/K), which is asymptotically optimal when K grows to infinity. For the online problem when the model parameters are unknown and need to be dynamically learned, we integrate the offline periodic policy with the upper confidence bound procedure to construct on online policy. The proposed online policy is proved to approximately have mathcal O(NT) regret against the offline benchmark. Our framework and policy design may shed light on broader offline planning and online learning applications with non-stationary and recovering rewards.

We tackle the problem of online reward maximisation over a large finite set of actions described by their contexts. We focus on the case when the number of actions is too big to sample all of them even once. However we assume that we have access to the similarities between actions' contexts and that the expected reward is an arbitrary linear function of the contexts' images in the related reproducing kernel Hilbert space (RKHS). We propose KernelUCB, a kernelised UCB algorithm, and give a cumulative regret bound through a frequentist analysis. For contextual bandits, the related algorithm GP-UCB turns out to be a special case of our algorithm, and our finite-time analysis improves the regret bound of GP-UCB for the agnostic case, both in the terms of the kernel-dependent quantity and the RKHS norm of the reward function. Moreover, for the linear kernel, our regret bound matches the lower bound for contextual linear bandits.

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1-delta, over the entire horizon of time T, each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm {\sc PASCombUCB} that minimizes the regret over the horizon of time T. By developing accompanying information-theoretic lower bounds, we show that under both the problem-dependent and problem-independent paradigms, {\sc PASCombUCB} is almost asymptotically optimal. Experiments are conducted to corroborate our theoretical findings. Our problem setup, the proposed {\sc PASCombUCB} algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.

We study a distributed stochastic multi-armed bandit where a client supplies the learner with communication-constrained feedback based on the rewards for the corresponding arm pulls. In our setup, the client must encode the rewards such that the second moment of the encoded rewards is no more than P, and this encoded reward is further corrupted by additive Gaussian noise of variance sigma^2; the learner only has access to this corrupted reward. For this setting, we derive an information-theoretic lower bound of Omegaleft(frac{KT{SNR wedge1}} right) on the minimax regret of any scheme, where SNR := P{sigma^2}, and K and T are the number of arms and time horizon, respectively. Furthermore, we propose a multi-phase bandit algorithm, UEtext{-UCB++}, which matches this lower bound to a minor additive factor. UEtext{-UCB++} performs uniform exploration in its initial phases and then utilizes the {\em upper confidence bound }(UCB) bandit algorithm in its final phase. An interesting feature of UEtext{-UCB++} is that the coarser estimates of the mean rewards formed during a uniform exploration phase help to refine the encoding protocol in the next phase, leading to more accurate mean estimates of the rewards in the subsequent phase. This positive reinforcement cycle is critical to reducing the number of uniform exploration rounds and closely matching our lower bound.

Recommender systems play a crucial role in internet economies by connecting users with relevant products. However, designing effective recommender systems faces the key challenges: the exploration-exploitation tradeoff in securing incentive to explore new products against user's self-interested preferences. While prior work addresses Bayesian Incentive Compatibility (BIC) in fixed-design linear bandits (Sellke & Slivkins, 2023), we tackle the challenge of stochastic user covariates sampled online. Unlike standard black-box reductions (Mansour et al., 2020), our two-stage framework exploits the linear reward structure to achieve sublinear regret while satisfying incentive constraints. To address it, we propose a two-stage algorithm that integrates incentivized exploration with any efficient plug-in offline learning algorithms. In the first stage, it explores products while maintaining incentive compatibility to gather optimal samples. The second stage employs inverse proportional gap sampling strategy (IPGS) integrated with any efficient learning methods to secure sublinear regret. Theoretically, we prove that algorithm RCB achieves O(KdT) regret and simultaneously satisfies incentive constraints, and discovers the tradeoff between incentive budget and regret, validating in experiments. We demonstrate RCB's strong incentive gain, sublinear regret, and robustness through a real application on personalized warfarin dosing and simulations.

Despite their success in many domains, large language models (LLMs) remain under-studied in scenarios requiring optimal decision-making under uncertainty. This is crucial as many real-world applications, ranging from personalized recommendations to healthcare interventions, demand that LLMs not only predict but also actively learn to make optimal decisions through exploration. In this work, we measure LLMs' (in)ability to make optimal decisions in bandits, a state-less reinforcement learning setting relevant to many applications. We develop a comprehensive suite of environments, including both context-free and contextual bandits with varying task difficulties, to benchmark LLMs' performance. Motivated by the existence of optimal exploration algorithms, we propose efficient ways to integrate this algorithmic knowledge into LLMs: by providing explicit algorithm-guided support during inference; and through algorithm distillation via in-context demonstrations and fine-tuning, using synthetic data generated from these algorithms. Impressively, these techniques allow us to achieve superior exploration performance with smaller models, surpassing larger models on various tasks. We conducted an extensive ablation study to shed light on various factors, such as task difficulty and data representation, that influence the efficiency of LLM exploration. Additionally, we conduct a rigorous analysis of the LLM's exploration efficiency using the concept of regret, linking its ability to explore to the model size and underlying algorithm.

We consider the linear contextual multi-class multi-period packing problem (LMMP) where the goal is to pack items such that the total vector of consumption is below a given budget vector and the total value is as large as possible. We consider the setting where the reward and the consumption vector associated with each action is a class-dependent linear function of the context, and the decision-maker receives bandit feedback. LMMP includes linear contextual bandits with knapsacks and online revenue management as special cases. We establish a new estimator which guarantees a faster convergence rate, and consequently, a lower regret in such problems. We propose a bandit policy that is a closed-form function of said estimated parameters. When the contexts are non-degenerate, the regret of the proposed policy is sublinear in the context dimension, the number of classes, and the time horizon T when the budget grows at least as T. We also resolve an open problem posed by Agrawal & Devanur (2016) and extend the result to a multi-class setting. Our numerical experiments clearly demonstrate that the performance of our policy is superior to other benchmarks in the literature.

We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate hatβ of the hidden parameter β^{star} of an underlying linear model. The key challenge of this work lies in the heteroscedasticity assumption that we make, meaning that each covariate has a different and unknown variance. The goal of the decision maker is then to figure out on the fly the optimal way to allocate the total budget of T samples between covariates, as sampling several times a specific one will reduce the variance of the estimated model around it (but at the cost of a possible higher variance elsewhere). By trying to minimize the ell^2-loss E [lVerthatβ-β^{star}rVert^2] the decision maker is actually minimizing the trace of the covariance matrix of the problem, which corresponds then to online A-optimal design. Combining techniques from bandit and convex optimization we propose a new active sampling algorithm and we compare it with existing ones. We provide theoretical guarantees of this algorithm in different settings, including a O(T^{-2}) regret bound in the case where the covariates form a basis of the feature space, generalizing and improving existing results. Numerical experiments validate our theoretical findings.

We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm BanditMLSM that attains O(T^{2/3}log T) of (1-1/e)-regret. Then we reduce submodular bandit with partition matroid constraint and bandit sequential monotone maximization to the online bandit learning of the monotone multi-linear DR-submodular functions, attaining O(T^{2/3}log T) of (1-1/e)-regret in both problems, which improve the existing results. To the best of our knowledge, we are the first to give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. A special case of this problem is studied by Streeter et al.(2009). They prove a O(T^{4/5}) (1-1/e)-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an O(T^{2/3}) regret with a suboptimal 1/2 approximation ratio (Niazadeh et al. 2021).

We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance tau. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision Processes (MDPs) setting. To extend CVaR RL to settings where state space is large, function approximation must be deployed. We study CVaR RL in low-rank MDPs with nonlinear function approximation. Low-rank MDPs assume the underlying transition kernel admits a low-rank decomposition, but unlike prior linear models, low-rank MDPs do not assume the feature or state-action representation is known. We propose a novel Upper Confidence Bound (UCB) bonus-driven algorithm to carefully balance the interplay between exploration, exploitation, and representation learning in CVaR RL. We prove that our algorithm achieves a sample complexity of Oleft(H^7 A^2 d^4{tau^2 epsilon^2}right) to yield an epsilon-optimal CVaR, where H is the length of each episode, A is the capacity of action space, and d is the dimension of representations. Computational-wise, we design a novel discretized Least-Squares Value Iteration (LSVI) algorithm for the CVaR objective as the planning oracle and show that we can find the near-optimal policy in a polynomial running time with a Maximum Likelihood Estimation oracle. To our knowledge, this is the first provably efficient CVaR RL algorithm in low-rank MDPs.

In many application domains (e.g., recommender systems, intelligent tutoring systems), the rewards associated to the actions tend to decrease over time. This decay is either caused by the actions executed in the past (e.g., a user may get bored when songs of the same genre are recommended over and over) or by an external factor (e.g., content becomes outdated). These two situations can be modeled as specific instances of the rested and restless bandit settings, where arms are rotting (i.e., their value decrease over time). These problems were thought to be significantly different, since Levine et al. (2017) showed that state-of-the-art algorithms for restless bandit perform poorly in the rested rotting setting. In this paper, we introduce a novel algorithm, Rotting Adaptive Window UCB (RAW-UCB), that achieves near-optimal regret in both rotting rested and restless bandit, without any prior knowledge of the setting (rested or restless) and the type of non-stationarity (e.g., piece-wise constant, bounded variation). This is in striking contrast with previous negative results showing that no algorithm can achieve similar results as soon as rewards are allowed to increase. We confirm our theoretical findings on a number of synthetic and dataset-based experiments.

Tabular data, structured as rows and columns, is among the most prevalent data types in machine learning classification and regression applications. Models for learning from tabular data have continuously evolved, with Deep Neural Networks (DNNs) recently demonstrating promising results through their capability of representation learning. In this survey, we systematically introduce the field of tabular representation learning, covering the background, challenges, and benchmarks, along with the pros and cons of using DNNs. We organize existing methods into three main categories according to their generalization capabilities: specialized, transferable, and general models. Specialized models focus on tasks where training and evaluation occur within the same data distribution. We introduce a hierarchical taxonomy for specialized models based on the key aspects of tabular data -- features, samples, and objectives -- and delve into detailed strategies for obtaining high-quality feature- and sample-level representations. Transferable models are pre-trained on one or more datasets and subsequently fine-tuned on downstream tasks, leveraging knowledge acquired from homogeneous or heterogeneous sources, or even cross-modalities such as vision and language. General models, also known as tabular foundation models, extend this concept further, allowing direct application to downstream tasks without fine-tuning. We group these general models based on the strategies used to adapt across heterogeneous datasets. Additionally, we explore ensemble methods, which integrate the strengths of multiple tabular models. Finally, we discuss representative extensions of tabular learning, including open-environment tabular machine learning, multimodal learning with tabular data, and tabular understanding. More information can be found in the following repository: https://github.com/LAMDA-Tabular/Tabular-Survey.

We revisit the standard perturbation-based approach of Abernethy et al. (2008) in the context of unconstrained Bandit Linear Optimization (uBLO). We show the surprising result that in the unconstrained setting, this approach effectively reduces Bandit Linear Optimization (BLO) to a standard Online Linear Optimization (OLO) problem. Our framework improves on prior work in several ways. First, we derive expected-regret guarantees when our perturbation scheme is combined with comparator-adaptive OLO algorithms, leading to new insights about the impact of different adversarial models on the resulting comparator-adaptive rates. We also extend our analysis to dynamic regret, obtaining the first guarantees with optimal P_T path-length dependencies without prior knowledge of P_T. We then develop the first high-probability guarantees for both static and dynamic regret in uBLO. Finally, we discuss lower bounds on the static regret, and prove the folklore Ω(dT) rate for adversarial linear bandits on the Euclidean ball, which is of independent interest.

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but the question is how, and by how much? We show that the degree of improvement must depend on the quality of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given competence level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

We consider the problem where an agent wants to find a hidden object that is randomly located in some vertex of a directed acyclic graph (DAG) according to a fixed but possibly unknown distribution. The agent can only examine vertices whose in-neighbors have already been examined. In this paper, we address a learning setting where we allow the agent to stop before having found the object and restart searching on a new independent instance of the same problem. Our goal is to maximize the total number of hidden objects found given a time budget. The agent can thus skip an instance after realizing that it would spend too much time on it. Our contributions are both to the search theory and multi-armed bandits. If the distribution is known, we provide a quasi-optimal and efficient stationary strategy. If the distribution is unknown, we additionally show how to sequentially approximate it and, at the same time, act near-optimally in order to collect as many hidden objects as possible.

Offline (or batch) reinforcement learning (RL) algorithms seek to learn an optimal policy from a fixed dataset without active data collection. Based on the composition of the offline dataset, two main categories of methods are used: imitation learning which is suitable for expert datasets and vanilla offline RL which often requires uniform coverage datasets. From a practical standpoint, datasets often deviate from these two extremes and the exact data composition is usually unknown a priori. To bridge this gap, we present a new offline RL framework that smoothly interpolates between the two extremes of data composition, hence unifying imitation learning and vanilla offline RL. The new framework is centered around a weak version of the concentrability coefficient that measures the deviation from the behavior policy to the expert policy alone. Under this new framework, we further investigate the question on algorithm design: can one develop an algorithm that achieves a minimax optimal rate and also adapts to unknown data composition? To address this question, we consider a lower confidence bound (LCB) algorithm developed based on pessimism in the face of uncertainty in offline RL. We study finite-sample properties of LCB as well as information-theoretic limits in multi-armed bandits, contextual bandits, and Markov decision processes (MDPs). Our analysis reveals surprising facts about optimality rates. In particular, in all three settings, LCB achieves a faster rate of 1/N for nearly-expert datasets compared to the usual rate of 1/N in offline RL, where N is the number of samples in the batch dataset. In the case of contextual bandits with at least two contexts, we prove that LCB is adaptively optimal for the entire data composition range, achieving a smooth transition from imitation learning to offline RL. We further show that LCB is almost adaptively optimal in MDPs.

Public repositories host millions of fine-tuned models, yet community usage remains disproportionately concentrated on a small number of foundation checkpoints. We investigate whether this concentration reflects efficient market selection or if superior models are systematically overlooked. Through an extensive evaluation of over 2,000 models, we show the prevalence of "hidden gems", unpopular fine-tunes that significantly outperform their popular counterparts. Notably, within the Llama-3.1-8B family, we find rarely downloaded checkpoints that improve math performance from 83.2% to 96.0% without increasing inference costs. However, discovering these models through exhaustive evaluation of every uploaded model is computationally infeasible. We therefore formulate model discovery as a Multi-Armed Bandit problem and accelerate the Sequential Halving search algorithm by using shared query sets and aggressive elimination schedules. Our method retrieves top models with as few as 50 queries per candidate, accelerating discovery by over 50x.

Despite the great interest in the bandit problem, designing efficient algorithms for complex models remains challenging, as there is typically no analytical way to quantify uncertainty. In this paper, we propose Multiplier Bootstrap-based Exploration (MBE), a novel exploration strategy that is applicable to any reward model amenable to weighted loss minimization. We prove both instance-dependent and instance-independent rate-optimal regret bounds for MBE in sub-Gaussian multi-armed bandits. With extensive simulation and real data experiments, we show the generality and adaptivity of MBE.

Learning on tabular data underpins numerous real-world applications. Despite considerable efforts in developing effective learning models for tabular data, current transferable tabular models remain in their infancy, limited by either the lack of support for direct instruction following in new tasks or the neglect of acquiring foundational knowledge and capabilities from diverse tabular datasets. In this paper, we propose Tabular Foundation Models (TabFMs) to overcome these limitations. TabFMs harness the potential of generative tabular learning, employing a pre-trained large language model (LLM) as the base model and fine-tuning it using purpose-designed objectives on an extensive range of tabular datasets. This approach endows TabFMs with a profound understanding and universal capabilities essential for learning on tabular data. Our evaluations underscore TabFM's effectiveness: not only does it significantly excel in instruction-following tasks like zero-shot and in-context inference, but it also showcases performance that approaches, and in instances, even transcends, the renowned yet mysterious closed-source LLMs like GPT-4. Furthermore, when fine-tuning with scarce data, our model achieves remarkable efficiency and maintains competitive performance with abundant training data. Finally, while our results are promising, we also delve into TabFM's limitations and potential opportunities, aiming to stimulate and expedite future research on developing more potent TabFMs.

This paper studies federated linear contextual bandits under the notion of user-level differential privacy (DP). We first introduce a unified federated bandits framework that can accommodate various definitions of DP in the sequential decision-making setting. We then formally introduce user-level central DP (CDP) and local DP (LDP) in the federated bandits framework, and investigate the fundamental trade-offs between the learning regrets and the corresponding DP guarantees in a federated linear contextual bandits model. For CDP, we propose a federated algorithm termed as ROBIN and show that it is near-optimal in terms of the number of clients M and the privacy budget varepsilon by deriving nearly-matching upper and lower regret bounds when user-level DP is satisfied. For LDP, we obtain several lower bounds, indicating that learning under user-level (varepsilon,delta)-LDP must suffer a regret blow-up factor at least min{1/varepsilon,M} or min{1/varepsilon,M} under different conditions.

For infinite action contextual bandits, smoothed regret and reduction to regression results in state-of-the-art online performance with computational cost independent of the action set: unfortunately, the resulting data exhaust does not have well-defined importance-weights. This frustrates the execution of downstream data science processes such as offline model selection. In this paper we describe an online algorithm with an equivalent smoothed regret guarantee, but which generates well-defined importance weights: in exchange, the online computational cost increases, but only to order smoothness (i.e., still independent of the action set). This removes a key obstacle to adoption of smoothed regret in production scenarios.