Document Type

Conference Proceeding

Publication Title

Proceedings of Machine Learning Research

Abstract

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity bounds are more accurate and less studied than in-expectation ones. However, SOTA high-probability non-asymptotic convergence results are derived under strong assumptions such as the boundedness of the gradient noise variance or of the objective's gradient itself. In this paper, we propose several algorithms with high-probability convergence results under less restrictive assumptions. In particular, we derive new high-probability convergence results under the assumption that the gradient/operator noise has bounded central α-th moment for α ∈ (1, 2] in the following setups: (i) smooth non-convex/Polyak-Łojasiewicz/convex/strongly convex/quasi-strongly convex minimization problems, (ii) Lipschitz/star-cocoercive and monotone/quasi-strongly monotone variational inequalities. These results justify the usage of the considered methods for solving problems that do not fit standard functional classes studied in stochastic optimization.

First Page

29563

Last Page

29648

Publication Date

7-2023

Keywords

Machine learning, Stochastic systems, Variational techniques

Comments

Open Access version from PMLR

Uploaded on May 31, 2024

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