The Power of First-Order Smooth Optimization for Black-Box Non-Smooth Problems
Abstract
Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration complexity, and propose a generic approach that, based on optimal first-order methods, allows to obtain in a black-box fashion new zeroth-order algorithms for non-smooth convex optimization problems. Our approach not only leads to optimal oracle complexity, but also allows to obtain iteration complexity similar to first-order methods, which, in turn, allows to exploit parallel computations to accelerate the convergence of our algorithms. We also elaborate on extensions for stochastic optimization problems, saddle-point problems, and distributed optimization.
Cite
@article{arxiv.2201.12289,
title = {The Power of First-Order Smooth Optimization for Black-Box Non-Smooth Problems},
author = {Alexander Gasnikov and Anton Novitskii and Vasilii Novitskii and Farshed Abdukhakimov and Dmitry Kamzolov and Aleksandr Beznosikov and Martin Takáč and Pavel Dvurechensky and Bin Gu},
journal= {arXiv preprint arXiv:2201.12289},
year = {2023}
}
Comments
Appears in: Proceedings of the 39th International Conference on Machine Learning (ICML 2022). Reference: https://proceedings.mlr.press/v162/gasnikov22a.html