Stochastic gradient descent ascent (SGDA) and its variants have been the workhorse for solving minimax problems. However, in contrast to the well-studied stochastic gradient descent (SGD) with differential privacy (DP) constraints, there is little work on understanding the generalization (utility) of SGDA with DP constraints. In this paper, we use the algorithmic stability approach to establish the generalization (utility) of DP-SGDA in different settings. In particular, for the convex-concave setting, we prove that the DP-SGDA can achieve an optimal utility rate in terms of the weak primal-dual population risk in both smooth and non-smooth cases. To our best knowledge, this is the first-ever-known result for DP-SGDA in the non-smooth case. We further provide its utility analysis in the nonconvex-strongly-concave setting which is the first-ever-known result in terms of the primal population risk. The convergence and generalization results for this nonconvex setting are new even in the non-private setting. Finally, numerical experiments are conducted to demonstrate the effectiveness of DP-SGDA for both convex and nonconvex cases.

翻译：在本文中,我们使用算法稳定性方法在不同环境中确定DP-SGDA的通用性(实用性),特别是对于凝聚层环境而言,我们证明DP-SGDA在光滑和非湿滑的个案中,在弱的初等人口风险方面能够达到最佳的实用率。据我们所知,这是DP-SGDA在非薄滑的个案中首次已知的结果。我们进一步在非凝固型的群落设置中提供了其实用性分析,这是在原始人口风险方面最先已知的结果。这种非凝聚型的组合和概括性设置在光滑滑和非湿滑的个案中都能达到最佳的实用率。就我们所知,这是DP-SGDA在非粗滑的个案中首次发现的结果。最后,我们在非凝结型非数字-DA的实验中展示了非数字-数字-DA的效益。