A Fast Algorithm for PAC Combinatorial Pure Exploration

TL;DR

This paper introduces a computationally efficient PAC combinatorial pure exploration algorithm capable of handling large-scale problems with tens of thousands of arms, significantly reducing the computational burden of previous methods.

Contribution

The paper presents a new lightweight PAC CPE algorithm that requires fewer combinatorial oracle calls, enabling practical application to large-scale problems.

Findings

The proposed algorithm has theoretical sample complexity guarantees.

It performs well on large problems in experiments, outperforming previous methods.

The algorithm is computationally feasible for problems with tens of thousands of arms.

Abstract

We consider the problem of Combinatorial Pure Exploration (CPE), which deals with finding a combinatorial set or arms with a high reward, when the rewards of individual arms are unknown in advance and must be estimated using arm pulls. Previous algorithms for this problem, while obtaining sample complexity reductions in many cases, are highly computationally intensive, thus making them impractical even for mildly large problems. In this work, we propose a new CPE algorithm in the PAC setting, which is computationally light weight, and so can easily be applied to problems with tens of thousands of arms. This is achieved since the proposed algorithm requires a very small number of combinatorial oracle calls. The algorithm is based on successive acceptance of arms, along with elimination which is based on the combinatorial structure of the problem. We provide sample complexity guarantees for our algorithm, and demonstrate in experiments its usefulness on large problems, whereas previous algorithms are impractical to run on problems of even a few dozen arms. The code for the algorithms and experiments is provided at https://github.com/noabdavid/csale.