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arXiv · 2606.01787

Stochastic convergence of parallel asynchronous adaptive first-order methods

Serge Gratton·Philippe L. Toint
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Abstract

A new class of asynchronous adaptive first-order optimization methods is introduced, comprising asynchronous variants of several popular algorithms. Versions of these methods using momentum and/or inexact normalization are also considered. The convergence of methods in the class on non-convex functions is analyzed in a fully stochastic setting, and is shown to be (up to logarithmic factors) of order O(1/sqrt{t}) under reasonable assumptions. Numerical experiments suggest that such asynchronous adaptive algorithms are very relevant in heterogeneous large-scale machine learning systems.

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Serge Gratton, Philippe L. Toint. 2026-06-01. Stochastic convergence of parallel asynchronous adaptive first-order methods. https://arxiv.org/abs/2606.01787

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