# Finding Second-Order Stationary Point for Nonconvex-Strongly-Concave Minimax Problem

@article{Luo2021FindingSS, title={Finding Second-Order Stationary Point for Nonconvex-Strongly-Concave Minimax Problem}, author={Luo Luo and Cheng Chen}, journal={ArXiv}, year={2021}, volume={abs/2110.04814} }

We study the smooth minimax optimization problem of the form minx maxy f(x,y), where the objective function is strongly-concave in y but possibly nonconvex in x. This problem includes a lot of applications in machine learning such as regularized GAN, reinforcement learning and adversarial training. Most of existing theory related to gradient descent accent focus on establishing the convergence result for achieving the first-order stationary point of f(x,y) or primal function P (x) , maxy f(x,y…

## 2 Citations

Faster Single-loop Algorithms for Minimax Optimization without Strong Concavity

- Computer Science, MathematicsArXiv
- 2021

New convergence results for two alternative single-loop algorithms – alternating GDA and smoothed GDA – under the mild assumption that the objective satisfies the PolyakLojasiewicz (PL) condition about one variable are established.

Fast Objective and Duality Gap Convergence for Non-convex Strongly-concave Min-max Problems

- Computer Science, MathematicsArXiv
- 2020

This paper considers leveraging the Polyak-Łojasiewicz (PL) condition to design faster stochastic algorithms with stronger convergence guarantee, and proposes and analyzes proximal epoch-based methods that establish fast convergence in terms of both primal objective gap and duality gap.

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