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Stochastic convergence of parallel asynchronous adaptive first-order methods

arXiv CS Tuesday 02 June 2026, 04:00 UTC By Serge Gratton, Philippe L. Toint 1 min read
Key Points

arXiv:2606.01787v1 Announce Type: new 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.

arXiv:2606.01787v1 Announce Type: new 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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