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We study private and robust multi-armed bandits (MABs), where the agent receives Huber's contaminated heavy-tailed rewards and meanwhile needs to ensure differential privacy. We first present its minimax lower bound, characterizing the…
We consider the exploration-exploitation tradeoff in linear quadratic (LQ) control problems, where the state dynamics is linear and the cost function is quadratic in states and controls. We analyze the regret of Thompson sampling (TS)…
Multi-armed bandit problems are considered as a paradigm of the trade-off between exploring the environment to find profitable actions and exploiting what is already known. In the stationary case, the distributions of the rewards do not…
As an extension of the classical multi-armed bandit problem, multi-fidelity multi-armed bandits (MF-MAB) enable individual arms to be evaluated using diverse feedback sources that vary in both cost and accuracy. Prior stochastic models…
We analyze the problem of sequential probability assignment for binary outcomes with side information and logarithmic loss, where regret---or, redundancy---is measured with respect to a (possibly infinite) class of experts. We provide upper…
Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better…
Multi-armed bandit methods have been used for dynamic experiments particularly in online services. Among the methods, thompson sampling is widely used because it is simple but shows desirable performance. Many thompson sampling methods for…
Adaptive and sequential experiment design is a well-studied area in numerous domains. We survey and synthesize the work of the online statistical learning paradigm referred to as multi-armed bandits integrating the existing research as a…
We present differentially private algorithms for the stochastic Multi-Armed Bandit (MAB) problem. This is a problem for applications such as adaptive clinical trials, experiment design, and user-targeted advertising where private…
We study a type of Multi-Armed Bandit (MAB) problems in which arms with a Gaussian reward feedback are clustered. Such an arm setting finds applications in many real-world problems, for example, mmWave communications and portfolio…
Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy,…
We study Thompson Sampling algorithms for stochastic multi-armed bandits in the batched setting, in which we want to minimize the regret over a sequence of arm pulls using a small number of policy changes (or, batches). We propose two…
This paper unifies the design and the analysis of risk-averse Thompson sampling algorithms for the multi-armed bandit problem for a class of risk functionals $\rho$ that are continuous and dominant. We prove generalised concentration bounds…
We study a generalization of the multi-armed bandit problem with multiple plays where there is a cost associated with pulling each arm and the agent has a budget at each time that dictates how much she can expect to spend. We derive an…
We study the stochastic linear bandit problem with multiple arms over $T$ rounds, where the covariate dimension $d$ may exceed $T$, but each arm-specific parameter vector is $s$-sparse. We begin by analyzing the sequential estimation…
We study the stochastic Multi-Armed Bandit (MAB) problem with random delays in the feedback received by the algorithm. We consider two settings: the reward-dependent delay setting, where realized delays may depend on the stochastic rewards,…
In this paper, we study the stochastic multi-armed bandit problem with graph feedback. Motivated by the clinical trials and recommendation problem, we assume that two arms are connected if and only if they are similar (i.e., their means are…
We discuss a multiple-play multi-armed bandit (MAB) problem in which several arms are selected at each round. Recently, Thompson sampling (TS), a randomized algorithm with a Bayesian spirit, has attracted much attention for its empirically…
In this paper, we study sequential testing problems with \emph{overlapping} hypotheses. We first focus on the simple problem of assessing if the mean $\mu$ of a Gaussian distribution is smaller or larger than a fixed $\epsilon>0$; if…
In the classical multi-armed bandit problem, d arms are available to the decision maker who pulls them sequentially in order to maximize his cumulative reward. Guarantees can be obtained on a relative quantity called regret, which scales…