  We analyze the convergence rates of stochastic gradient algorithms for smooth
finite-sum minimax optimization and show that, for many such algorithms,
sampling the data points without replacement leads to faster convergence
compared to sampling with replacement. For the smooth and strongly
convex-strongly concave setting, we consider gradient descent ascent and the
proximal point method, and present a unified analysis of two popular
without-replacement sampling strategies, namely Random Reshuffling (RR), which
shuffles the data every epoch, and Single Shuffling or Shuffle Once (SO), which
shuffles only at the beginning. We obtain tight convergence rates for RR and SO
and demonstrate that these strategies lead to faster convergence than uniform
sampling. Moving beyond convexity, we obtain similar results for smooth
nonconvex-nonconcave objectives satisfying a two-sided Polyak-{\L}ojasiewicz
inequality. Finally, we demonstrate that our techniques are general enough to
analyze the effect of data-ordering attacks, where an adversary manipulates the
order in which data points are supplied to the optimizer. Our analysis also
recovers tight rates for the incremental gradient method, where the data points
are not shuffled at all.
