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Stochastic gradient descent-ascent (SGDA) is one of the main workhorses forsolving finite-sum minimax optimization problems. Most practicalimplementations of SGDA randomly reshuffle components and sequentially use them(i.e., without-replacement sampling); however, there are few theoreticalresults on this approach for minimax algorithms, especially outside theeasier-to-analyze (strongly-)monotone setups. To narrow this gap, we study theconvergence bounds of SGDA with random reshuffling (SGDA-RR) for smoothnonconvex-nonconcave objectives with Polyak-{\L}ojasiewicz (P{\L}) geometry. Weanalyze both simultaneous and alternating SGDA-RR for nonconvex-P{\L} andprimal-P{\L}-P{\L} objectives, and obtain convergence rates faster thanwith-replacement SGDA. Our rates extend to mini-batch SGDA-RR, recovering knownrates for full-batch gradient descent-ascent (GDA). Lastly, we present acomprehensive lower bound for GDA with an arbitrary step-size ratio, whichmatches the full-batch upper bound for the primal-P{\L}-P{\L} case.

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