Convergence Rate of Payoff-based Generalized Nash Equilibrium Learning

Tatiana Tatarenko; Maryam Kamgarpour

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arXiv · 2411.08595

Convergence Rate of Payoff-based Generalized Nash Equilibrium Learning

Tatiana Tatarenko·Maryam Kamgarpour

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Abstract

We consider generalized Nash equilibrium (GNE) problems in games with strongly monotone pseudo-gradients and jointly linear coupling constraints. We establish the convergence rate of a payoff-based approach intended to learn a variational GNE (v-GNE) in such games. While convergent algorithms have recently been proposed in this setting given full or partial information of the gradients, rate of convergence in the payoff-based information setting has been an open problem. Leveraging properties of a game extended from the original one by a dual player, we establish a convergence rate of $O(\frac{1}{t^{4/7}})$ to a v-GNE of the game.

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Tatiana Tatarenko, Maryam Kamgarpour. 2024-11-13. Convergence Rate of Payoff-based Generalized Nash Equilibrium Learning. https://arxiv.org/abs/2411.08595

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