Corpus ID: 211044046

Near-Optimal Algorithms for Minimax Optimization

@article{Lin2020NearOptimalAF,
  title={Near-Optimal Algorithms for Minimax Optimization},
  author={Tianyi Lin and C. Jin and Michael I. Jordan},
  journal={ArXiv},
  year={2020},
  volume={abs/2002.02417}
}
This paper resolves a longstanding open question pertaining to the design of near-optimal first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems. Current state-of-the-art first-order algorithms find an approximate Nash equilibrium using $\tilde{O}(\kappa_{\mathbf x}+\kappa_{\mathbf y})$ or $\tilde{O}(\min\{\kappa_{\mathbf x}\sqrt{\kappa_{\mathbf y}}, \sqrt{\kappa_{\mathbf x}}\kappa_{\mathbf y}\})$ gradient evaluations, where $\kappa_{\mathbf x}$ and $\kappa_… Expand
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References

SHOWING 1-10 OF 107 REFERENCES
New Proximal Point Algorithms for Convex Minimization
  • O. Güler
  • Mathematics, Computer Science
  • SIAM J. Optim.
  • 1992
  • 177
Efficient Algorithms for Smooth Minimax Optimization
  • 60
  • Highly Influential
  • PDF
A Primal-Dual Algorithm for General Convex-Concave Saddle Point Problems
  • 43
  • Highly Influential
  • PDF
On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems
  • 111
  • PDF
Lower bounds for finding stationary points II: first-order methods
  • 43
  • PDF
Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods
  • 104
  • Highly Influential
  • PDF
Gradient methods for minimizing composite functions
  • Y. Nesterov
  • Mathematics, Computer Science
  • Math. Program.
  • 2013
  • 905
  • PDF
Optimal Algorithms for Stochastic Three-Composite Convex-Concave Saddle Point Problems
  • 9
  • PDF
Dual extrapolation and its applications to solving variational inequalities and related problems
  • Y. Nesterov
  • Mathematics, Computer Science
  • Math. Program.
  • 2007
  • 186
  • PDF
...
1
2
3
4
5
...