Related papers: Optimal Exploration is no harder than Thompson Sam…
We study the problem of best-arm identification with fixed confidence in stochastic linear bandits. The objective is to identify the best arm with a given level of certainty while minimizing the sampling budget. We devise a simple algorithm…
In model-based solution approaches to the problem of learning in an unknown environment, exploring to learn the model parameters takes a toll on the regret. The optimal performance with respect to regret or PAC bounds is achievable, if the…
We study the federated pure exploration problem of multi-armed bandits and linear bandits, where $M$ agents cooperatively identify the best arm via communicating with the central server. To enhance the robustness against latency and…
We consider the problem of the best arm identification in the presence of stochastic constraints, where there is a finite number of arms associated with multiple performance measures. The goal is to identify the arm that optimizes the…
We study the logistic bandit, in which rewards are binary with success probability $\exp(\beta a^\top \theta) / (1 + \exp(\beta a^\top \theta))$ and actions $a$ and coefficients $\theta$ are within the $d$-dimensional unit ball. While prior…
How can we make use of information parallelism in online decision making problems while efficiently balancing the exploration-exploitation trade-off? In this paper, we introduce a batch Thompson Sampling framework for two canonical online…
An asymptotically optimal sampling-based planner employs sampling to solve robot motion planning problems and returns paths with a cost that converges to the optimal solution cost, as the number of samples approaches infinity. This…
We consider the problem of statistical inference when the data is collected via a Thompson Sampling-type algorithm. While Thompson Sampling (TS) is known to be both asymptotically optimal and empirically effective, its adaptive sampling…
The design and performance analysis of bandit algorithms in the presence of stage-wise safety or reliability constraints has recently garnered significant interest. In this work, we consider the linear stochastic bandit problem under…
This paper proposes near-optimal algorithms for the pure-exploration linear bandit problem in the fixed confidence and fixed budget settings. Leveraging ideas from the theory of suprema of empirical processes, we provide an algorithm whose…
In this paper we propose a general methodology to derive regret bounds for randomized multi-armed bandit algorithms. It consists in checking a set of sufficient conditions on the sampling probability of each arm and on the family of…
This work addresses the problem of regret minimization in non-stochastic multi-armed bandit problems, focusing on performance guarantees that hold with high probability. Such results are rather scarce in the literature since proving them…
Thompson Sampling, one of the oldest heuristics for solving multi-armed bandits, has recently been shown to demonstrate state-of-the-art performance. The empirical success has led to great interests in theoretical understanding of this…
We study stochastic structured bandits for minimizing regret. The fact that the popular optimistic algorithms do not achieve the asymptotic instance-dependent regret optimality (asymptotic optimality for short) has recently alluded…
This note introduce three Bayesian style Multi-armed bandit algorithms: Information-directed sampling, Thompson Sampling and Generalized Thompson Sampling. The goal is to give an intuitive explanation for these three algorithms and their…
We consider the thresholding bandit problem, whose goal is to find arms of mean rewards above a given threshold $\theta$, with a fixed budget of $T$ trials. We introduce LSA, a new, simple and anytime algorithm that aims to minimize the…
Thompson sampling (TS) is widely used for stochastic multi-armed bandits, yet its inferential properties under adaptive data collection are subtle. Classical asymptotic theory for sample means can fail because arm-specific sample sizes are…
Approximate Thompson sampling with Langevin Monte Carlo broadens its reach from Gaussian posterior sampling to encompass more general smooth posteriors. However, it still encounters scalability issues in high-dimensional problems when…
We consider the problem of Active Search, where a maximum of relevant objects - ideally all relevant objects - should be retrieved with the minimum effort or minimum time. Typically, there are two main challenges to face when tackling this…
This paper studies the Bayesian regret of the Thompson Sampling algorithm for bandit problems, building on the information-theoretic framework introduced by Russo and Van Roy (2015). Specifically, it extends the rate-distortion analysis of…