Adversarial bandit optimization for approximately linear functions
Machine Learning
2026-01-07 v8 Artificial Intelligence
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.
Cite
@article{arxiv.2505.20734,
title = {Adversarial bandit optimization for approximately linear functions},
author = {Zhuoyu Cheng and Kohei Hatano and Eiji Takimoto},
journal= {arXiv preprint arXiv:2505.20734},
year = {2026}
}