This paper studies the uniform convergence and generalization bounds for nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization. We first establish the uniform convergence between the empirical minimax problem and the population minimax problem and show the $\tilde{\mathcal{O}}(d\kappa^2\epsilon^{-2})$ and $\tilde{\mathcal{O}}(d\epsilon^{-4})$ sample complexities respectively for the NC-SC and NC-C settings, where $d$ is the dimension number and $\kappa$ is the condition number. To the best of our knowledge, this is the first uniform convergence measured by the first-order stationarity in stochastic minimax optimization. Based on the uniform convergence, we shed light on the sample and gradient complexities required for finding an approximate stationary point for stochastic minimax optimization in the NC-SC and NC-C settings.

翻译：本文分别研究了非混凝土(强力)混凝土(NC-SC/NC-C)混凝土(NC-SC/NC-C)的样本复杂性。 我们首先确定了经验微型最大问题与人口微型最大问题的统一趋同,并展示了美元(tilde)和美元(mathcal{O})(d\kappa ⁇ 2\\epsilon ⁇ 2})和美元(d\epsilon ⁇ 4})的(d\silon})和NC-C(NC)的样本复杂性。 在NC-SC和NC-C的设置中,美元是维数,而$(kappa)是条件数。 据我们所知,这是以随机小型最大优化的第一阶定点测量的首次统一趋同。基于统一趋同,我们介绍了在NCSCC和NC的设置中,为找到一个近似固定点进行微混凝胶优化所需的样本和梯度复杂性。