Gaussian Process Classification Bandits

TL;DR

This paper introduces a Gaussian process-based classification bandit framework with novel policies that improve sample efficiency in classifying arms, outperforming existing methods in synthetic and real-world experiments.

Contribution

It develops a new framework and policies, FCB and FTSV, for Gaussian process classification bandits with improved sample complexity bounds and empirical performance.

Findings

FCB has a smaller sample complexity upper bound than existing level set estimation algorithms.

Rate-estimation policies outperform other policies in synthetic function experiments.

FTSV achieves the best performance on a real-world dataset.

Abstract

Classification bandits are multi-armed bandit problems whose task is to classify a given set of arms into either positive or negative class depending on whether the rate of the arms with the expected reward of at least h is not less than w for given thresholds h and w. We study a special classification bandit problem in which arms correspond to points x in d-dimensional real space with expected rewards f(x) which are generated according to a Gaussian process prior. We develop a framework algorithm for the problem using various arm selection policies and propose policies called FCB and FTSV. We show a smaller sample complexity upper bound for FCB than that for the existing algorithm of the level set estimation, in which whether f(x) is at least h or not must be decided for every arm's x. Arm selection policies depending on an estimated rate of arms with rewards of at least h are also proposed and shown to improve empirical sample complexity. According to our experimental results, the rate-estimation versions of FCB and FTSV, together with that of the popular active learning policy that selects the point with the maximum variance, outperform other policies for synthetic functions, and the version of FTSV is also the best performer for our real-world dataset.