Fixed-Budget Constrained Best Arm Identification in Grouped Bandits

TL;DR

This paper introduces a new algorithm for fixed-budget best-arm identification in grouped bandits, ensuring feasibility and optimality in identifying the best arm with all attributes above a threshold.

Contribution

It proposes FCSR, a novel algorithm that guarantees feasibility and achieves optimal error bounds, advancing the understanding of constrained bandit problems.

Findings

FCSR outperforms baseline algorithms in empirical tests.

FCSR attains near-optimal error probability bounds.

Theoretical lower bounds are established for the problem.

Abstract

We study fixed budget constrained best-arm identification in grouped bandits, where each arm consists of multiple independent attributes with stochastic rewards. An arm is considered feasible only if all its attributes' means are above a given threshold. The aim is to find the feasible arm with the largest overall mean. We first derive a lower bound on the error probability for any algorithm on this setting. We then propose Feasibility Constrained Successive Rejects (FCSR), a novel algorithm that identifies the best arm while ensuring feasibility. We show it attains optimal dependence on problem parameters up to constant factors in the exponent. Empirically, FCSR outperforms natural baselines while preserving feasibility guarantees.