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- W4383046626 abstract "Nonconvex-nonconcave minimax problems have found numerous applications in various fields including machine learning. However, questions remain about what is a good surrogate for local minimax optimum and how to characterize the minimax optimality. Recently Jin, Netrapalli, and Jordan (ICML 2020) introduced a concept of local minimax point and derived optimality conditions for the smooth and unconstrained case. In this paper, we introduce the concept of calm local minimax point, which is a local minimax point with a calm radius function. With the extra calmness property we obtain first and second-order sufficient and necessary optimality conditions for a very general class of nonsmooth nonconvex-nonconcave minimax problem. Moreover we show that the calm local minimax optimality and the local minimax optimality coincide under a weak sufficient optimality condition for the maximization problem. This equivalence allows us to derive stronger optimality conditions under weaker assumptions for local minimax optimality." @default.
- W4383046626 created "2023-07-04" @default.
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- W4383046626 date "2023-06-30" @default.
- W4383046626 modified "2023-09-26" @default.
- W4383046626 title "Calm local optimality for nonconvex-nonconcave minimax problems" @default.
- W4383046626 doi "https://doi.org/10.48550/arxiv.2306.17443" @default.
- W4383046626 hasPublicationYear "2023" @default.
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