  This paper takes an initial step to systematically investigate the
generalization bounds 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
$\epsilon$-generalization are $\tilde{\mathcal{O}}(d\kappa^2\epsilon^{-2})$ and
$\tilde{\mathcal{O}}(d\epsilon^{-4})$ for NC-SC and NC-C settings,
respectively, where $d$ is the dimension and $\kappa$ 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 generalization bounds and
the stability notion. As a result, we establish algorithm-dependent
generalization bounds for stochastic gradient descent ascent (SGDA) algorithm
and the more general sampling-determined algorithms.
