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Adaptive extra-gradient methods for min-max optimization and games

Abstract : We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation mechanism, the proposed method automatically detects whether the problem is smooth or not, without requiring any prior tuning by the optimizer. As a result, the algorithm simultaneously achieves order-optimal convergence rates, i.e., it converges to an ε-optimal solution within O(1/ε) iterations in smooth problems, and within O(1/ε 2) iterations in non-smooth ones.Importantly, these guarantees do not require any of the standard boundedness or Lipschitz continuity conditions that are typically assumed in the literature; in particular, they apply even to problems with singularities (such as resource allocation problems and the like). This adaptation is achieved through the use of a geometric apparatus based on Finsler metrics and a suitably chosen mirror-prox template that allows us to derive sharp convergence rates for the methods at hand.
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https://hal.inria.fr/hal-03342601
Contributor : Panayotis Mertikopoulos Connect in order to contact the contributor
Submitted on : Monday, September 13, 2021 - 2:47:44 PM
Last modification on : Friday, October 22, 2021 - 4:36:50 AM

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  • HAL Id : hal-03342601, version 1

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Kimon Antonakopoulos, Veronica Belmega, Panayotis Mertikopoulos. Adaptive extra-gradient methods for min-max optimization and games. ICLR 2021 - 9th International Conference on Learning Representations, May 2021, Virtual, Unknown Region. pp.1-28. ⟨hal-03342601⟩

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