Related papers: Non-Asymptotic Pure Exploration by Solving Games
We investigate an active pure-exploration setting, that includes best-arm identification, in the context of linear stochastic bandits. While asymptotically optimal algorithms exist for standard multi-arm bandits, the existence of such…
We determine the sample complexity of pure exploration bandit problems with multiple good answers. We derive a lower bound using a new game equilibrium argument. We show how continuity and convexity properties of single-answer problems…
Given a set of arms $\mathcal{Z}\subset \mathbb{R}^d$ and an unknown parameter vector $\theta_\ast\in\mathbb{R}^d$, the pure exploration linear bandit problem aims to return $\arg\max_{z\in \mathcal{Z}} z^{\top}\theta_{\ast}$, with high…
In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are…
Combinatorial bandits with semi-bandit feedback generalize multi-armed bandits, where the agent chooses sets of arms and observes a noisy reward for each arm contained in the chosen set. The action set satisfies a given structure such as…
We propose a new strategy for best-arm identification with fixed confidence of Gaussian variables with bounded means and unit variance. This strategy, called Exploration-Biased Sampling, is not only asymptotically optimal: it is to the best…
We study pure exploration with infinitely many bandit arms generated i.i.d. from an unknown distribution. Our goal is to efficiently select a single high quality arm whose average reward is, with probability $1-\delta$, within $\varepsilon$…
We study the combinatorial pure exploration problem Best-Set in stochastic multi-armed bandits. In a Best-Set instance, we are given $n$ arms with unknown reward distributions, as well as a family $\mathcal{F}$ of feasible subsets over the…
We propose the first fully-adaptive algorithm for pure exploration in linear bandits---the task to find the arm with the largest expected reward, which depends on an unknown parameter linearly. While existing methods partially or entirely…
While experimental design often focuses on selecting the single best alternative from a finite set (e.g., in ranking and selection or best-arm identification), many pure-exploration problems pursue richer goals. Given a specific goal,…
Pure exploration in multi-armed bandits has emerged as an important framework for modeling decision-making and search under uncertainty. In modern applications, however, one is often faced with a tremendously large number of options. Even…
In pure exploration problems, a statistician sequentially collects information to answer a question about some stochastic and unknown environment. The probability of returning a wrong answer should not exceed a maximum risk parameter…
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…
Pure exploration in bandits formalises multiple real-world problems, such as tuning hyper-parameters or conducting user studies to test a set of items, where different safety, resource, and fairness constraints on the decision space…
We study a specific \textit{combinatorial pure exploration stochastic bandit problem} where the learner aims at finding the set of arms whose means are above a given threshold, up to a given precision, and \textit{for a fixed time horizon}.…
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…
Motivated by an open direction in existing literature, we study the 1-identification problem, a fundamental multi-armed bandit formulation on pure exploration. The goal is to determine whether there exists an arm whose mean reward is at…
We address the problem of identifying the optimal policy with a fixed confidence level in a multi-armed bandit setup, when \emph{the arms are subject to linear constraints}. Unlike the standard best-arm identification problem which is well…
We study the sample complexity of identifying the pure strategy Nash equilibrium (PSNE) in a two-player zero-sum matrix game with noise. Formally, we are given a stochastic model where any learner can sample an entry $(i,j)$ of the input…
We study pure exploration problems in which the set of correct answers is possibly infinite. For example, such problems arise when regressing a continuous function on the means of the bandit or when learning Nash equilibria by querying…