Adversarial bandit optimization for approximately linear functions

TL;DR

This paper introduces an adversarial bandit optimization framework for approximately linear functions, providing regret bounds and a lower bound, advancing understanding of nonconvex, non-smooth bandit problems.

Contribution

It develops regret bounds for a new class of bandit problems with perturbations and improves bounds for bandit linear optimization, also establishing a lower bound on expected regret.

Findings

Expected and high-probability regret bounds derived.

Improved high-probability regret bound for bandit linear optimization.

Lower bound on expected regret established.

Abstract

We consider a bandit optimization problem for nonconvex and non-smooth functions, where in each trial the loss function is the sum of a linear function and a small but arbitrary perturbation chosen after observing the player's choice. We give both expected and high probability regret bounds for the problem. Our result also implies an improved high-probability regret bound for the bandit linear optimization, a special case with no perturbation. We also give a lower bound on the expected regret.