Nonlinearly Preconditioned Gradient Methods: Momentum and Stochastic Analysis

Konstantinos Oikonomidis, Jan Quan, Panagiotis Patrinos

Keywords: non-convex optimization, stochastic optimization

Domains: Other

External Link: https://tinyurl.com/3utyancc

Abstract: We study nonlinearly preconditioned gradient methods for smooth nonconvex optimization problems, focusing on sigmoid preconditioners that inherently perform a form of gradient clipping akin to the widely used gradient clipping technique. Building upon this idea, we introduce a novel heavy ball-type algorithm and provide convergence guarantees under a generalized smoothness condition that is less restrictive than traditional Lipschitz smoothness, thus covering a broader class of functions. Additionally, we develop a stochastic variant of the base method and study its convergence properties under different noise assumptions. We compare the proposed algorithms with baseline methods on diverse tasks from machine learning including neural network training. This paper was presented at NeurIPS 2025, https://tinyurl.com/3utyancc.

Submission Number: 106