Differentially Private SGDA for Minimax Problems
This work addresses privacy concerns in machine learning for minimax optimization, providing foundational theoretical guarantees for DP-SGDA, which is incremental but includes first-known results for non-smooth and nonconvex cases.
The paper tackles the problem of ensuring differential privacy in stochastic gradient descent ascent (SGDA) for minimax problems, establishing generalization bounds and achieving optimal utility rates in convex-concave and nonconvex-strongly-concave settings, with numerical experiments validating effectiveness.
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.