Improved convergence rate of sgda by shuffling: focusing on the nonconvex-PŁ minimax problems

Abstract

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 upper bounds 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-PŁ-PŁ case.

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)