SGDA with shuffling: faster convergence for nonconvex-P{\L} minimax optimization

• URL: http://arxiv.org/abs/2210.05995v1
• Date: Wed, 12 Oct 2022 08:05:41 GMT
• Title: SGDA with shuffling: faster convergence for nonconvex-P{\L} minimax optimization
• Authors: Hanseul Cho, Chulhee Yun
• Abstract summary: We present a theoretical approach for solving minimax optimization problems using sequentially descent-ascent gradient (SGDA) We analyze both simultaneous and alternating SGDA-LL objectives for non-concave objectives with Polyak-Lojasiewicz (PL) geometry. Our rates also extend to mini-batch-GDARR, recovering few known rates for full gradient-batch descent-ascent gradient (GDA) Finally, we present a comprehensive lower bound for two-time-scale GDA, which matches the full rate for primal-PL-
• Score: 18.668531108219415
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stochastic gradient descent-ascent (SGDA) is one of the main workhorses for solving finite-sum minimax optimization problems. Most practical implementations of SGDA randomly reshuffle components and sequentially use them (i.e., without-replacement sampling); however, there are few theoretical results on this approach for minimax algorithms, especially outside the easier-to-analyze (strongly-)monotone setups. To narrow this gap, we study the convergence bounds of SGDA with random reshuffling (SGDA-RR) for smooth nonconvex-nonconcave objectives with Polyak-{\L}ojasiewicz (P{\L}) geometry. We analyze both simultaneous and alternating SGDA-RR for nonconvex-P{\L} and primal-P{\L}-P{\L} objectives, and obtain convergence rates faster than with-replacement SGDA. Our rates also extend to mini-batch SGDA-RR, recovering known rates for full-batch gradient descent-ascent (GDA). Lastly, we present a comprehensive lower bound for two-time-scale GDA, which matches the full-batch rate for primal-P{\L}-P{\L} case.

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