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Communication Dans Un Congrès Année : 2022

Last-Iterate Convergence of Optimistic Gradient Method for Monotone Variational Inequalities

Résumé

The Past Extragradient (PEG) [Popov, 1980] method, also known as the Optimistic Gradient method, has known a recent gain in interest in the optimization community with the emergence of variational inequality formulations for machine learning. Recently, in the unconstrained case, Golowich et al. [2020] proved that a $O(1/N)$ last-iterate convergence rate in terms of the squared norm of the operator can be achieved for Lipschitz and monotone operators with a Lipschitz Jacobian. In this work, by introducing a novel analysis through potential functions, we show that (i) this $O(1/N)$ last-iterate convergence can be achieved without any assumption on the Jacobian of the operator, and (ii) it can be extended to the constrained case, which was not derived before even under Lipschitzness of the Jacobian. The proof is significantly different from the one known from Golowich et al. [2020], and its discovery was computer-aided. Those results close the open question of the last iterate convergence of PEG for monotone variational inequalities.

Dates et versions

hal-03780329 , version 1 (19-09-2022)

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Citer

Eduard Gorbunov, Adrien Taylor, Gauthier Gidel. Last-Iterate Convergence of Optimistic Gradient Method for Monotone Variational Inequalities. NeurIPS 2022 - Thirty-sixth Conference on Neural Information Processing Systems, Nov 2022, New orleans, United States. ⟨hal-03780329⟩
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