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Bibliographic Details
Main Authors: Lobanov, Aleksandr, Gasnikov, Alexander
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2307.12725
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Table of Contents:
  • This paper is devoted to solving a convex stochastic optimization problem in a overparameterization setup for the case where the original gradient computation is not available, but an objective function value can be computed. For this class of problems we provide a novel gradient-free algorithm, whose creation approach is based on applying a gradient approximation with $l_2$ randomization instead of a gradient oracle in the biased Accelerated SGD algorithm, which generalizes the convergence results of the AC-SA algorithm to the case where the gradient oracle returns a noisy (inexact) objective function value. We also perform a detailed analysis to find the maximum admissible level of adversarial noise at which we can guarantee to achieve the desired accuracy. We verify the theoretical results of convergence using a model example.