Nearly Optimal Best Arm Identification for Semiparametric Bandits

TL;DR

This paper introduces a nearly optimal algorithm for fixed-confidence best arm identification in semiparametric bandits, addressing an open problem with theoretical guarantees and empirical validation.

Contribution

It presents a new phase-elimination algorithm based on an $XY$-design, achieving near-optimal sample complexity for semiparametric bandits.

Findings

The algorithm attains a nearly optimal high-probability sample complexity bound.

Experiments demonstrate significant improvements over prior methods.

Theoretical analysis matches the linear-bandit complexity on shifted features.

Abstract

We study fixed-confidence Best Arm Identification (BAI) in semiparametric bandits, where rewards are linear in arm features plus an unknown additive baseline shift. Unlike linear-bandit BAI, this setting requires orthogonalized regression, and its instance-optimal sample complexity has remained open. For the transductive setting, we establish an attainable instance-dependent lower bound characterized by the corresponding linear-bandit complexity on shifted features. We then propose a computationally efficient phase-elimination algorithm based on a new $XY$-design for orthogonalized regression. Our analysis yields a nearly optimal high-probability sample-complexity upper bound, up to log factors and an additive $d^2$ term, and experiments on synthetic instances and the Jester dataset show clear gains over prior baselines.