We study the greedy (exploitation-only) algorithm in bandit problems with a known reward structure. We allow arbitrary finite reward structures, while prior work focused on a few specific ones. We fully characterize when the greedy algorithm asymptotically succeeds or fails, in the sense of sublinear vs. linear regret as a function of time. Our characterization identifies a partial identifiability property of the problem instance as the necessary and sufficient condition for the asymptotic success. Notably, once this property holds, the problem becomes easy--any algorithm will succeed (in the same sense as above), provided it satisfies a mild non-degeneracy condition. Our characterization extends to contextual bandits and interactive decision-making with arbitrary feedback. Examples demonstrating broad applicability and extensions to infinite reward structures are provided.

We consider the problem of identifying the best arm in a multi-armed bandit model. Despite a wealth of literature in the traditional fixed budget and fixed confidence regimes of the best arm identification problem, it still remains a mystery to most practitioners as to how to choose an approach and corresponding budget or confidence parameter. We propose a new formalism to avoid this dilemma altogether by minimizing a risk functional which explicitly balances the performance of the recommended arm and the cost incurred by learning this arm. In this framework, a cost is incurred for each observation during the sampling phase, and upon recommending an arm, a performance penalty is incurred for identifying a suboptimal arm. The learner's goal is to minimize the sum of the penalty and cost. This new regime mirrors the priorities of many practitioners, e.g.

In multi-armed bandits with network interference (MABNI), the action taken by one node can influence the rewards of others, creating complex interdependence. While existing research on MABNI largely concentrates on minimizing regret, it often overlooks the crucial concern that an excessive emphasis on the optimal arm can undermine the inference accuracy for sub-optimal arms. Although initial efforts have been made to address this trade-off in single-unit scenarios, these challenges have become more pronounced in the context of MABNI. In this paper, we establish, for the first time, a theoretical Pareto frontier characterizing the trade-off between regret minimization and inference accuracy in adversarial (design-based) MABNI. We further introduce an anytime-valid asymptotic confidence sequence along with a corresponding algorithm, EXP3-N-CS, specifically designed to balance the trade-off between regret minimization and inference accuracy in this setting.

Traditional curriculum learning proceeds from easy to hard samples, yet defining a reliable notion of difficulty remains elusive. Prior work has used submodular functions to induce difficulty scores in curriculum learning. We reinterpret adaptive subset selection and formulate it as a multi-armed bandit problem, where each arm corresponds to a submodular function guiding sample selection. We introduce ONLINESUBMOD, a novel online greedy policy that optimizes a utility-driven reward and provably achieves no-regret performance under various sampling regimes. Empirically, ONLINESUBMOD outperforms both traditional curriculum learning and bi-level optimization approaches across vision and language datasets, showing superior accuracy-efficiency tradeoffs. More broadly, we show that validationdriven reward metrics offer a principled way to guide the curriculum schedule. Our code is publicly available at GitHub 2.

We consider a common case of the combinatorial semi-bandit problem, the m-set semi-bandit, where the learner exactly selects m arms from the total d arms. In the adversarial setting, the best regret bound, known to be O( nmd) for time horizon n, is achieved by the well-known Follow-the-Regularized-Leader (FTRL) policy. However, this requires to explicitly compute the arm-selection probabilities via optimizing problems at each time step and sample according to them. This problem can be avoided by the Follow-the-Perturbed-Leader (FTPL) policy, which simply pulls the m arms that rank among the m smallest (estimated) loss with random perturbation. In this paper, we show that FTPL with a Fréchet perturbation also enjoys the near optimal regret bound O( nm( p dlog(d) + m5/6)) in the adversarial setting and approaches best-of-both-world regret bounds, i.e., achieves a logarithmic regret for the stochastic setting. Moreover, our lower bounds show that the extra factors are unavoidable with our approach; any improvement would require a fundamentally different and more challenging method.

Best Arm Identification (BAI) algorithms are deployed in data-sensitive applications, such as adaptive clinical trials or user studies. Driven by the privacy concerns of these applications, we study the problem of fixed-confidence BAI under global Differential Privacy (DP) for Bernoulli distributions. While numerous asymptotically optimal BAI algorithms exist in the non-private setting, a significant gap remains between the best lower and upper bounds in the global DP setting. This work reduces this gap to a small multiplicative constant, for any privacy budget ϵ. First, we provide a tighter lower bound on the expected sample complexity of any δ-correct and ϵ-global DP strategy.

In real-world decision-making problems, one needs to pick among multiple policies the one that performs best while respecting economic constraints. This motivates the problem of constrained best-arm identification for bandit problems where every arm is a joint distribution of reward and cost. We investigate the general case where reward and cost are dependent. The goal is to accurately identify the arm with the highest mean reward among all arms whose mean cost is below a given threshold. We prove information-theoretic lower bounds on the sample complexity for three models: Gaussian with fixed covariance, Gaussian with unknown covariance, and non-parametric distributions of rectangular support. We propose a combination of a sampling and a stopping rule that correctly identifies the constrained best arm and matches the optimal sample complexities for each of the three models. Simulations demonstrate the performance of our algorithms.

We consider a stochastic multi-armed bandit problem with i.i.d.

This paper addresses the problem of multi-risk measure agnostic multi-armed bandits in heavy-tailed reward settings. We propose a framework that leverages novel deviation inequalities for the 1-Wasserstein distance to construct confidence intervals for Lipschitz risk measures. The distributional LCB (DistLCB) algorithm is introduced, which achieves asymptotic optimality by deriving the first lower bounds for risk measure aware bandits with explicit sub-optimality gap dependencies. The DistLCB is further extended to multi-risk objectives, which enables Pareto-optimal solutions that consider multiple aspects of reward distributions. Additionally, we provide a regret analysis that includes both gap-dependent and gap-independent bounds for multi-risk settings. Experiments validate the effectiveness of the proposed methods in synthetic and real-world applications.

We study matching markets with ties, where workers on one side of the market may have tied preferences over jobs, determined by their matching utilities. Unlike classical two-sided markets with strict preferences, no single stable matching exists that is utility-maximizing for all workers. To address this challenge, we introduce the Optimal Stable Share (OSS)-ratio, which measures the ratio of a worker's maximum achievable utility in any stable matching to their utility in a given matching. We prove that distributions over only stable matchings can incur linear utility losses, i.e., an Ω(N) OSS-ratio, where N is the number of workers. To overcome this, we design an algorithm that efficiently computes a distribution over (possibly non-stable) matchings, achieving an asymptotically tight O(logN) OSS-ratio. When exact utilities are unknown, our second algorithm guarantees workers a logarithmic approximation of their optimal utility under bounded instability. Finally, we extend our offline approximation results to a bandit learning setting where utilities are only observed for matched pairs. In this setting, we consider worker-optimal stable regret, design an adaptive algorithm that smoothly interpolates between markets with strict preferences and those with statistical ties, and establish a lower bound revealing the fundamental trade-off between strict and tied preference regimes.