שיטות מואצות עם פחת-אופטימום לבעיות מינימקס חזק-קונבקס

תקציר מקורי באנגליתarXiv:2307.07113v2 Announce Type: replace-cross Abstract: In this paper, we consider the decentralized, stochastic nonconvex strongly-concave (NCSC) minimax problem with nonsmooth regularization terms on both primal and dual variables, wherein a network of $m$ computing agents collaborate via peer-to-peer communications. We consider when the coupling function is in expectation or finite-sum form and the double regularizers are convex functions, applied separately to the primal and dual variables. Our algorithmic framework introduces a Lagrangian multiplier to eliminate the consensus constraint on the dual variable. Coupling this with variance-reduction (VR) techniques, our proposed method, entitled VRLM, by a single neighbor communication per iteration, is able to achieve an $\mathcal{O}(\