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The growing size of available data has attracted increasing interest insolving minimax problems in a decentralized manner for various machine learningtasks. Previous theoretical research has primarily focused on the convergencerate and communication complexity of decentralized minimax algorithms, withlittle attention given to their generalization. In this paper, we investigatethe primal-dual generalization bound of the decentralized stochastic gradientdescent ascent (D-SGDA) algorithm using the approach of algorithmic stabilityunder both convex-concave and nonconvex-nonconcave settings. Our theory refinesthe algorithmic stability in a decentralized manner and demonstrates that thedecentralized structure does not destroy the stability and generalization ofD-SGDA, implying that it can generalize as well as the vanilla SGDA in certainsituations. Our results analyze the impact of different topologies on thegeneralization bound of the D-SGDA algorithm beyond trivial factors such assample sizes, learning rates, and iterations. We also evaluate the optimizationerror and balance it with the generalization gap to obtain the optimalpopulation risk of D-SGDA in the convex-concave setting. Additionally, weperform several numerical experiments which validate our theoretical findings.

Stability and Generalization of the Decentralized Stochastic Gradient Descent Ascent Algorithm