An optimal algorithm for the Thresholding Bandit Problem

TL;DR

This paper introduces an optimal, parameter-free algorithm for the combinatorial pure exploration stochastic bandit problem with a fixed budget, providing the first such strategy with proven optimality.

Contribution

It presents the first non-trivial fixed-budget pure exploration algorithm with proven optimality in the combinatorial bandit setting.

Findings

Algorithm is proven to be optimal through matching bounds.

First non-trivial fixed-budget pure exploration strategy with optimality.

Provides theoretical guarantees for the proposed method.

Abstract

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 propose a parameter-free algorithm based on an original heuristic, and prove that it is optimal for this problem by deriving matching upper and lower bounds. To the best of our knowledge, this is the first non-trivial pure exploration setting with \textit{fixed budget} for which optimal strategies are constructed.