Fixed-Budget Best-Arm Identification in Structured Bandits

TL;DR

This paper introduces a new algorithm for fixed-budget best-arm identification in structured bandit models, leveraging model-based elimination and G-optimal design, with theoretical guarantees and practical performance in linear and generalized linear models.

Contribution

It presents the first practical fixed-budget BAI algorithm with analysis for generalized linear models, extending structured bandit methods beyond linear settings.

Findings

Competitive error guarantees in linear models

First practical fixed-budget BAI algorithm for GLMs

Empirical performance matches theoretical analysis

Abstract

Best-arm identification (BAI) in a fixed-budget setting is a bandit problem where the learning agent maximizes the probability of identifying the optimal (best) arm after a fixed number of observations. Most works on this topic study unstructured problems with a small number of arms, which limits their applicability. We propose a general tractable algorithm that incorporates the structure, by successively eliminating suboptimal arms based on their mean reward estimates from a joint generalization model. We analyze our algorithm in linear and generalized linear models (GLMs), and propose a practical implementation based on a G-optimal design. In linear models, our algorithm has competitive error guarantees to prior works and performs at least as well empirically. In GLMs, this is the first practical algorithm with analysis for fixed-budget BAI.