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Solving Non-Convex Non-Differentiable Min-Max Games using Proximal Gradient Method
- Publication Year :
- 2020
-
Abstract
- Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special convex-concave structure. While some recent works generalized these results to special smooth non-convex cases, our understanding of non-smooth scenarios is still limited. In this work, we study special form of non-smooth min-max games when the objective function is (strongly) convex with respect to one of the player's decision variable. We show that a simple multi-step proximal gradient descent-ascent algorithm converges to $\epsilon$-first-order Nash equilibrium of the min-max game with the number of gradient evaluations being polynomial in $1/\epsilon$. We will also show that our notion of stationarity is stronger than existing ones in the literature. Finally, we evaluate the performance of the proposed algorithm through adversarial attack on a LASSO estimator.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2003.08093
- Document Type :
- Working Paper