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

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.-generalization are (O) over tilde (d kappa(2)epsilon(-2)) and (O) over tilde (d epsilon(-4)) for NC-SC and NC-C settings, respectively, where d is the dimension of the primal variable and. 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).