Limiting Behaviors of Nonconvex-Nonconcave Minimax Optimization via Continuous-Time Systems

What is local optimality in nonconvex-nonconcave minimax optimization?

Jin, C., Netrapalli, P., and Jordan, M. I. (2020) · 1902

Earlier work this paper cites.

The stable, center-stable, center, center-unstable, unstable manifolds

Kelley, A. (1967) · 1967

Earlier work this paper cites.

On minimax robustness: A general approach and applications

Verdu, S. and Poor, H. (1984) · 1984

Earlier work this paper cites.

Elements of Applied Bifurcation Theory (2nd Ed.)

Kuznetsov, Y. A. (1998) · 1998

Earlier work this paper cites.

An o ⁡ ( s r ) o(s^{r}) -resolution ode framework for discrete-time optimization algorithms and applications to the linear convergence of minimax problems

Lu, H. (2020) · 2001

Earlier work this paper cites.

Global convergence and variance-reduced optimization for a class of nonconvex-nonconcave minimax problems

Yang, J., Kiyavash, N., and He, N. (2020) · 2002

Earlier work this paper cites.

On the impossibility of global convergence in multi-loss optimization

Letcher, A. (2020) · 2005

Earlier work this paper cites.

The landscape of the proximal point method for nonconvex-nonconcave minimax optimization

Grimmer, B., Lu, H., Worah, P., and Mirrokni, V. (2020) · 2006

Earlier work this paper cites.

The limits of min-max optimization algorithms: convergence to spurious non-critical sets

Hsieh, Y.-P., Mertikopoulos, P., and Cevher, V. (2020) · 2006

Cited alongside, same era.

Robust optimization

Ben-Tal, A., El Ghaoui, L., and Nemirovski, A. (2009) · 2009

Cited alongside, same era.

Theory and applications of robust optimization

Bertsimas, D., Brown, D. B., and Caramanis, C. (2011) · 2011

Cited alongside, same era.

Generative adversarial nets

Goodfellow, I. J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. (2014) · 2014

Cited alongside, same era.

Saddle-point dynamics: conditions for asymptotic stability of saddle points

Cherukuri, A., Gharesifard, B., and Cortes, J. (2016) · 2016

Cited alongside, same era.

A differential equation for modeling nesterov’s accelerated gradient method: Theory and insights

Su, W., Boyd, S., and Candès, E. J. (2016) · 2016

Solving weakly-convex-weakly-concave saddle-point problems as successive strongly monotone variational inequalities

Lin, Q., Liu, M., Rafique, H., and Yang, T. (2018) · 2018

Later among the works it cites.

Understanding the acceleration phenomenon via high-resolution differential equations

Shi, B., Du, S. S., Jordan, M. I., and Su, W. J. (2018) · 2018

Later among the works it cites.

Local saddle point optimization: A curvature exploitation approach

Adolphs, L., Daneshmand, H., Lucchi, A., and Hofmann, T. (2019) · 2019

Later among the works it cites.

Interaction matters: A note on non-asymptotic local convergence of generative adversarial networks

Liang, T. and Stokes, J. (2019) · 2019

Later among the works it cites.

Solving a class of non-convex min-max games using iterative first order methods

Nouiehed, M., Sanjabi, M., Huang, T., Lee, J. D., and Razaviyayn, M. (2019) · 2019

Later among the works it cites.