A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits

TL;DR

This paper introduces RGP-PE, a robust algorithm for Gaussian process bandit optimization that effectively handles adversarial corruptions, providing tighter regret bounds and demonstrating empirical robustness.

Contribution

The paper proposes a novel robust elimination algorithm for corrupted GP bandits with improved theoretical regret bounds and empirical validation of robustness.

Findings

Regret bound improves to O(C γ_T^{3/2}) from O(C √T γ_T)

Algorithm demonstrates robustness against various adversarial attacks

First empirical study of robustness in corrupted GP bandit setting

Abstract

We consider the sequential optimization of an unknown, continuous, and expensive to evaluate reward function, from noisy and adversarially corrupted observed rewards. When the corruption attacks are subject to a suitable budget $C$ and the function lives in a Reproducing Kernel Hilbert Space (RKHS), the problem can be posed as corrupted Gaussian process (GP) bandit optimization. We propose a novel robust elimination-type algorithm that runs in epochs, combines exploration with infrequent switching to select a small subset of actions, and plays each action for multiple time instants. Our algorithm, Robust GP Phased Elimination (RGP-PE), successfully balances robustness to corruptions with exploration and exploitation such that its performance degrades minimally in the presence (or absence) of adversarial corruptions. When $T$ is the number of samples and $\gamma_T$ is the maximal information gain, the corruption-dependent term in our regret bound is $O(C \gamma_T^{3/2})$, which is significantly tighter than the existing $O(C \sqrt{T \gamma_T})$ for several commonly-considered kernels. We perform the first empirical study of robustness in the corrupted GP bandit setting, and show that our algorithm is robust against a variety of adversarial attacks.