Accelerated Zeroth-Order Method for Non-Smooth Stochastic Convex Optimization Problem with Infinite Variance
Abstract
In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the batched accelerated gradient method, was proposed in (Gasnikov et. al., 2022). This optimality is defined in terms of iteration and oracle complexity, as well as the maximal admissible level of adversarial noise. However, the assumption of finite variance is burdensome and it might not hold in many practical scenarios. To address this, we demonstrate how to adapt a refined clipped version of the accelerated gradient (Stochastic Similar Triangles) method from (Sadiev et al., 2023) for a two-point zero-order oracle. This adaptation entails extending the batching technique to accommodate infinite variance — a non-trivial task that stands as a distinct contribution of this paper.
Cite
Text
Kornilov et al. "Accelerated Zeroth-Order Method for Non-Smooth Stochastic Convex Optimization Problem with Infinite Variance." Neural Information Processing Systems, 2023.Markdown
[Kornilov et al. "Accelerated Zeroth-Order Method for Non-Smooth Stochastic Convex Optimization Problem with Infinite Variance." Neural Information Processing Systems, 2023.](https://mlanthology.org/neurips/2023/kornilov2023neurips-accelerated/)BibTeX
@inproceedings{kornilov2023neurips-accelerated,
title = {{Accelerated Zeroth-Order Method for Non-Smooth Stochastic Convex Optimization Problem with Infinite Variance}},
author = {Kornilov, Nikita and Shamir, Ohad and Lobanov, Aleksandr and Dvinskikh, Darina and Gasnikov, Alexander and Shibaev, Innokentiy and Gorbunov, Eduard and Horváth, Samuel},
booktitle = {Neural Information Processing Systems},
year = {2023},
url = {https://mlanthology.org/neurips/2023/kornilov2023neurips-accelerated/}
}