GRADIENT-FREE ALGORITHMS FOR SOLVING STOCHASTIC SADDLE OPTIMIZATION PROBLEMS WITH THE POLYAK–LOYASIEVICH CONDITION-Reference-Cited by-同舟云学术

GRADIENT-FREE ALGORITHMS FOR SOLVING STOCHASTIC SADDLE OPTIMIZATION PROBLEMS WITH THE POLYAK–LOYASIEVICH CONDITION

Published:2023-11-01 Issue:6 Volume: Page:60-74
ISSN:0132-3474
Container-title:Программирование
language:
Short-container-title:Programmirovanie

Author:

Sadykov S. I.¹,Lobanov A. V.¹²,Raigorodskii A. M.¹³

Affiliation:

1. Moscow Institute of Physics and Technology

2. Trusted Artificial Intelligence Research Center of ISP RAS

3. Caucasian Mathematical Center of the Adyghe State University

Abstract

This paper focuses on solving a subclass of a stochastic nonconvex-concave black box optimization problem with a saddle point that satisfies the Polyak–Loyasievich condition. To solve such a problem, we provide the first, to our knowledge, gradient-free algorithm, the approach to which is based on applying a gradient approximation (kernel approximation) to the oracle-shifted stochastic gradient descent algorithm. We present theoretical estimates that guarantee a global linear rate of convergence to the desired accuracy. We check the theoretical results on a model example, comparing with an algorithm using Gaussian approximation.

Publisher

The Russian Academy of Sciences

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