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Mathematics > Optimization and Control

arXiv:2210.05995 (math)
[Submitted on 12 Oct 2022 (v1), last revised 20 Feb 2023 (this version, v2)]

Title:SGDA with shuffling: faster convergence for nonconvex-PŁ minimax optimization

Authors:Hanseul Cho, Chulhee Yun
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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-Łojasiewicz (PŁ) geometry. We analyze both simultaneous and alternating SGDA-RR for nonconvex-PŁ and primal-PŁ-PŁ objectives, and obtain convergence rates faster than with-replacement SGDA. Our rates extend to mini-batch SGDA-RR, recovering known rates for full-batch gradient descent-ascent (GDA). Lastly, we present a comprehensive lower bound for GDA with an arbitrary step-size ratio, which matches the full-batch upper bound for the primal-PŁ-PŁ case.
Comments: ICLR 2023 camera-ready version; 46 pages
Subjects: Optimization and Control (math.OC); Machine Learning (stat.ML)
Cite as: arXiv:2210.05995 [math.OC]
  (or arXiv:2210.05995v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.05995

Submission history

From: Hanseul Cho [view email]
[v1] Wed, 12 Oct 2022 08:05:41 UTC (65 KB)
[v2] Mon, 20 Feb 2023 10:18:32 UTC (7,014 KB)
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