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Poster

Generalization Bounds of Nonconvex-(Strongly)-Concave Stochastic Minimax Optimization

Siqi Zhang · Yifan Hu · Liang Zhang · Niao He

MR1 & MR2 - Number 165

Abstract: This paper studies the generalization performance of algorithms for solving nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization measured by the stationarity of primal functions. We first establish algorithm-agnostic generalization bounds via uniform convergence between the empirical minimax problem and the population minimax problem. The sample complexities for achieving ϵϵ-generalization are ˜O(dκ2ϵ2)~O(dκ2ϵ2) and ˜O(dϵ4)~O(dϵ4) for NC-SC and NC-C settings, respectively, where dd is the dimension of the primal variable and κκ is the condition number. We further study the algorithm-dependent generalization bounds via stability arguments of algorithms. In particular, we introduce a novel stability notion for minimax problems and build a connection between stability and generalization. As a result, we establish algorithm-dependent generalization bounds for stochastic gradient descent ascent (SGDA) and the more general sampling-determined algorithms (SDA).

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