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.
View on arXiv@article{cheng2025_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={ 2025 }
}