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We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the `Track-and-Stop' strategy, which we prove to be…
Combinatorial Multi-Armed Bandit with fairness constraints is a framework where multiple arms form a super arm and can be pulled in each round under uncertainty to maximize cumulative rewards while ensuring the minimum average reward…
Scientific experimentation is largely driven by statistical hypothesis testing to determine significant differences in interventions. Traditionally, experimenters allocate samples uniformly between each intervention. However, such an…
We consider the problem of identifying the best arm in stochastic Multi-Armed Bandits (MABs) using a fixed sampling budget. Characterizing the minimal instance-specific error probability for this problem constitutes one of the important…
We consider a non-stationary formulation of the stochastic multi-armed bandit where the rewards are no longer assumed to be identically distributed. For the best-arm identification task, we introduce a version of Successive Elimination…
We study the problem of finding the optimal dosage in early stage clinical trials through the multi-armed bandit lens. We advocate the use of the Thompson Sampling principle, a flexible algorithm that can accommodate different types of…
This paper introduces a general multi-agent bandit model in which each agent is facing a finite set of arms and may communicate with other agents through a central controller in order to identify, in pure exploration, or play, in regret…
We introduce the model selection problem in pure exploration linear bandits, where the learner needs to adapt to the instance-dependent complexity measure of the smallest hypothesis class containing the true model. We design algorithms in…
Many real-world functions are defined over both categorical and category-specific continuous variables and thus cannot be optimized by traditional Bayesian optimization (BO) methods. To optimize such functions, we propose a new method that…
The combinatorial stochastic semi-bandit problem is an extension of the classical multi-armed bandit problem in which an algorithm pulls more than one arm at each stage and the rewards of all pulled arms are revealed. One difference with…
Combinatorial bandits extend the classical bandit framework to settings where the learner selects multiple arms in each round, motivated by applications such as online recommendation and assortment optimization. While extensions of upper…
In the Best-$K$ identification problem (Best-$K$-Arm), we are given $N$ stochastic bandit arms with unknown reward distributions. Our goal is to identify the $K$ arms with the largest means with high confidence, by drawing samples from the…
Much of the recent literature on bandit learning focuses on algorithms that aim to converge on an optimal action. One shortcoming is that this orientation does not account for time sensitivity, which can play a crucial role when learning an…
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 {\epsilon}-best arms (i.e., those at most {\epsilon} worse than…
We propose EB-TC$\varepsilon$, a novel sampling rule for $\varepsilon$-best arm identification in stochastic bandits. It is the first instance of Top Two algorithm analyzed for approximate best arm identification. EB-TC$\varepsilon$ is an…
We present an algorithm, "constrained successive accept or reject (CSAR)," for the problem of identifying the subset of top feasible-arms from a given finite set of arms with the limited sampling-budget equal to a given time-horizon when…
Thompson Sampling has been widely used for contextual bandit problems due to the flexibility of its modeling power. However, a general theory for this class of methods in the frequentist setting is still lacking. In this paper, we present a…
In pure-exploration problems, information is gathered sequentially to answer a question on the stochastic environment. While best-arm identification for linear bandits has been extensively studied in recent years, few works have been…
There has been a recent surge of interest in nonparametric bandit algorithms based on subsampling. One drawback however of these approaches is the additional complexity required by random subsampling and the storage of the full history of…
Thompson sampling is a popular algorithm for solving multi-armed bandit problems, and has been applied in a wide range of applications, from website design to portfolio optimization. In such applications, however, the number of choices (or…