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The classic multi-armed bandit (MAB) problem tackles the challenge of accruing maximum reward while making decisions under uncertainty. However, in applications, often the goal is to minimize cost subject to a constraint on the minimum…
The knowledge gradient (KG) algorithm is a popular and effective algorithm for the best arm identification (BAI) problem. Due to the complex calculation of KG, theoretical analysis of this algorithm is difficult, and existing results are…
Motivated by recursive learning in Markov Decision Processes, this paper studies best-arm identification in bandit problems where each arm's reward is drawn from a multinomial distribution with a known support. We compare the performance {…
We consider the multi armed bandit problem in non-stationary environments. Based on the Bayesian method, we propose a variant of Thompson Sampling which can be used in both rested and restless bandit scenarios. Applying discounting to the…
We study the real-valued combinatorial pure exploration of the multi-armed bandit in the fixed-budget setting. We first introduce the Combinatorial Successive Asign (CSA) algorithm, which is the first algorithm that can identify the best…
Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization. We study a quantum computational version of this problem with coherent oracle access to states encoding the reward probabilities of each arm as…
Given a vector of probability distributions, or arms, each of which can be sampled independently, we consider the problem of identifying the partition to which this vector belongs from a finitely partitioned universe of such vector of…
We study the pure exploration problem subject to a matroid constraint (Best-Basis) in a stochastic multi-armed bandit game. In a Best-Basis instance, we are given $n$ stochastic arms with unknown reward distributions, as well as a matroid…
We consider a novel stochastic multi-armed bandit setting, where playing an arm makes it unavailable for a fixed number of time slots thereafter. This models situations where reusing an arm too often is undesirable (e.g. making the same…
Motivated by drug design, we consider the best-arm identification problem in generalized linear bandits. More specifically, we assume each arm has a vector of covariates, there is an unknown vector of parameters that is common across the…
We study exploration in stochastic multi-armed bandits when we have access to a divisible resource that can be allocated in varying amounts to arm pulls. We focus in particular on the allocation of distributed computing resources, where we…
When an experimenter has the option of running an adaptive trial, is it admissible to ignore this option and run a non-adaptive trial instead? We provide a negative answer to this question in the best-arm identification problem, where the…
This paper focuses on best-arm identification in multi-armed bandits with bounded rewards. We develop an algorithm that is a fusion of lil-UCB and KL-LUCB, offering the best qualities of the two algorithms in one method. This is achieved by…
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…
We investigate the sample complexity of learning the optimal arm for multi-task bandit problems. Arms consist of two components: one that is shared across tasks (that we call representation) and one that is task-specific (that we call…
Thompson sampling is one of the earliest randomized algorithms for multi-armed bandits (MAB). In this paper, we extend the Thompson sampling to Budgeted MAB, where there is random cost for pulling an arm and the total cost is constrained by…
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 stochastic linear optimization problem with bandit feedback. The set of arms take values in an $N$-dimensional space and belong to a bounded polyhedron described by finitely many linear inequalities. We provide a lower bound for…
We consider a decision maker allocating one unit of renewable and divisible resource in each period on a number of arms. The arms have unknown and random rewards whose means are proportional to the allocated resource and whose variances are…
The question of selecting the "best" amongst different choices is a common problem in statistics. In drug development, our motivating setting, the question becomes, for example: what is the dose that gives me a pre-specified risk of…