Optimal Best Arm Identification with Fixed Confidence

TL;DR

This paper characterizes the complexity of best-arm identification in one-parameter bandit problems, introduces a tight lower bound on sample complexity, and proposes an asymptotically optimal 'Track-and-Stop' strategy with a novel sampling rule and analysis.

Contribution

It provides a complete characterization of the problem's complexity, a new tight lower bound, and an optimal strategy with proven asymptotic optimality.

Findings

Established a tight lower bound on sample complexity.

Proposed the 'Track-and-Stop' strategy with a novel sampling rule.

Proved asymptotic optimality of the proposed method.

Abstract

We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the `Track-and-Stop' strategy, which we prove to be asymptotically optimal. It consists in a new sampling rule (which tracks the optimal proportions of arm draws highlighted by the lower bound) and in a stopping rule named after Chernoff, for which we give a new analysis.