mlsanityData to 14 Oct 2026

Two-timescale Extragradient for Finding Local Minimax Points

arXiv 2305.16242 ↗First posted 25 May 2023math.OC cs.LGcited by 4

Not on the map. Why?

Abstract (arXiv)

Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the second-order necessary condition of local minimax points, under mild conditions that the two-timescale gradient descent ascent fails to work. This work provably improves upon all previous results on finding local minimax points, by eliminating a crucial assumption that the Hessian with respect to the maximization variable is nondegenerate.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 15 of its 45 references that are in the map. First posted on arXiv 25 May 2023.

Builds on

15 of 45 references.

References · 15

  1. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  2. 2022Generative Adversarial Networkscited by 5,627
  3. 2020Sharpness-Aware Minimization for Efficiently Improving Generalizationcited by 1,417
  4. 2018Which Training Methods for GANs do actually Converge?cited by 679
  5. 2016NIPS 2016 Tutorial: Generative Adversarial Networkscited by 285
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  7. 2018The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimizationcited by 101
  8. 2020Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimizationcited by 96
  9. 2019On Solving Minimax Optimization Locally: A Follow-the-Ridge Approachcited by 34
  10. 2019ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problemscited by 18
  11. 2022Convergence of Proximal Point and Extragradient-Based Methods Beyond Monotonicity: the Case of Negative Comonotonicitycited by 16
  12. 2020Newton-type Methods for Minimax Optimizationcited by 11
3 more
  1. 2022Tight Analysis of Extra-gradient and Optimistic Gradient Methods For Nonconvex Minimax Problemscited by 7
  2. 2021A Cubic Regularization Approach for Finding Local Minimax Points in Nonconvex Minimax Optimizationcited by 5
  3. 2020Optimality and Stability in Non-Convex Smooth Gamescited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 1.

4 papers.

  1. 2025Negative Stepsizes Make Gradient-Descent-Ascent Convergecited by 11
  2. 2025Properties of Fixed Points of Generalised Extra Gradient Methods Applied to Min-Max Problemscited by 3
  3. 2025Min-Max Optimization Is Strictly Easier Than Variational Inequalitiescited by 1
  4. 2026On the Stability Connection Between Discrete-Time Algorithms and Their Resolution ODEs: Applications to Min-Max Optimisationcited by 1