Continuous-time Discounted Mirror-Descent Dynamics in Monotone Concave Games
Abstract
In this paper, we consider concave continuous-kernel games characterized by monotonicity properties and propose discounted mirror descent-type dynamics. We introduce two classes of dynamics whereby the associated mirror map is constructed based on a strongly convex or a Legendre regularizer. Depending on the properties of the regularizer we show that these new dynamics can converge asymptotically in concave games with monotone (negative) pseudo-gradient. Furthermore, we show that when the regularizer enjoys strong convexity, the resulting dynamics can converge even in games with hypo-monotone (negative) pseudo-gradient, which corresponds to a shortage of monotonicity.
Keywords
Cite
@article{arxiv.1912.03460,
title = {Continuous-time Discounted Mirror-Descent Dynamics in Monotone Concave Games},
author = {Bolin Gao and Lacra Pavel},
journal= {arXiv preprint arXiv:1912.03460},
year = {2024}
}
Comments
8 pages, 9 figures. This work has been submitted to the IEEE for possible publication