Asymptotically Optimal Linear Best Feasible Arm Identification with Fixed Budget

TL;DR

This paper introduces a new algorithm for best feasible arm identification in linear bandits that achieves the optimal exponential decay rate of error probability, matching theoretical bounds, and outperforms existing methods.

Contribution

The paper presents a novel posterior sampling-based algorithm with a game-theoretic sampling rule that guarantees optimal error decay rate in fixed-budget linear bandit problems.

Findings

The algorithm achieves the exponential decay rate matching the theoretical lower bound.

Empirical results show superior accuracy and efficiency over benchmark algorithms.

The approach extends Thompson sampling principles to fixed-budget best arm identification.

Abstract

The challenge of identifying the best feasible arm within a fixed budget has attracted considerable interest in recent years. However, a notable gap remains in the literature: the exact exponential rate at which the error probability approaches zero has yet to be established, even in the relatively simple setting of $K$-armed bandits with Gaussian noise. In this paper, we address this gap by examining the problem within the context of linear bandits. We introduce a novel algorithm for best feasible arm identification that guarantees an exponential decay in the error probability. Remarkably, the decay rate -- characterized by the exponent -- matches the theoretical lower bound derived using information-theoretic principles. Our approach leverages a posterior sampling framework embedded within a game-based sampling rule involving a min-learner and a max-learner. This strategy shares its foundations with Thompson sampling, but is specifically tailored to optimize the identification process under fixed-budget constraints. Furthermore, we validate the effectiveness of our algorithm through comprehensive empirical evaluations across various problem instances with different levels of complexity. The results corroborate our theoretical findings and demonstrate that our method outperforms several benchmark algorithms in terms of both accuracy and efficiency.