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arXiv · 2202.11147

On the Rate of Convergence of Payoff-based Algorithms to Nash Equilibrium in Strongly Monotone Games

Tatiana Tatarenko·Maryam Kamgarpour
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Abstract

We derive the rate of convergence to Nash equilibria for the payoff-based algorithm proposed in \cite{tat_kam_TAC}. These rates are achieved under the standard assumption of convexity of the game, strong monotonicity and differentiability of the pseudo-gradient. In particular, we show the algorithm achieves $O(\frac{1}{T})$ in the two-point function evaluating setting and $O(\frac{1}{\sqrt{T}})$ in the one-point function evaluation under additional requirement of Lipschitz continuity of the pseudo-gradient. These rates are to our knowledge the best known rates for the corresponding problem classes.

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Tatiana Tatarenko, Maryam Kamgarpour. 2022-02-22. On the Rate of Convergence of Payoff-based Algorithms to Nash Equilibrium in Strongly Monotone Games. https://arxiv.org/abs/2202.11147

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