Bandit Convex Optimisation Revisited: FTRL Achieves $\tilde{O}(t^{1/2})$ Regret

TL;DR

This paper demonstrates that a kernel estimator can be adapted into a sampling-based bandit estimator, enabling the FTRL algorithm to achieve near-optimal regret bounds in adversarial convex optimization settings.

Contribution

It introduces a novel method to convert kernel estimators into bandit estimators and applies this to improve regret bounds for FTRL in bandit convex optimization.

Findings

Achieves  O(t^{1/2}) regret with FTRL in bandit convex optimization.

Provides a simple conversion of kernel estimators into bandit estimators.

Enhances the theoretical understanding of bandit algorithms with kernel methods.

Abstract

We show that a kernel estimator using multiple function evaluations can be easily converted into a sampling-based bandit estimator with expectation equal to the original kernel estimate. Plugging such a bandit estimator into the standard FTRL algorithm yields a bandit convex optimisation algorithm that achieves $\tilde{O}(t^{1/2})$ regret against adversarial time-varying convex loss functions.