Min-Max Optimization under Delays

• URL: http://arxiv.org/abs/2307.06886v3
• Date: Fri, 25 Aug 2023 03:14:32 GMT
• Title: Min-Max Optimization under Delays
• Authors: Arman Adibi, Aritra Mitra, and Hamed Hassani
• Abstract summary: Delays and asynchrony are inevitable in large-scale machine-learning problems. No analogous theory is available for min-max optimization. We show that even small delays can cause prominent algorithms like Extra-gradient to diverge.
• Score: 26.830212508878162
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Delays and asynchrony are inevitable in large-scale machine-learning problems where communication plays a key role. As such, several works have extensively analyzed stochastic optimization with delayed gradients. However, as far as we are aware, no analogous theory is available for min-max optimization, a topic that has gained recent popularity due to applications in adversarial robustness, game theory, and reinforcement learning. Motivated by this gap, we examine the performance of standard min-max optimization algorithms with delayed gradient updates. First, we show (empirically) that even small delays can cause prominent algorithms like Extra-gradient (\texttt{EG}) to diverge on simple instances for which \texttt{EG} guarantees convergence in the absence of delays. Our empirical study thus suggests the need for a careful analysis of delayed versions of min-max optimization algorithms. Accordingly, under suitable technical assumptions, we prove that Gradient Descent-Ascent (\texttt{GDA}) and \texttt{EG} with delayed updates continue to guarantee convergence to saddle points for convex-concave and strongly convex-strongly concave settings. Our complexity bounds reveal, in a transparent manner, the slow-down in convergence caused by delays.

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