Continuous-Time Discounted Mirror Descent Dynamics in Monotone Concave Games
Bolin Gao, Lacra Pavel · IEEE Transactions on Automatic Control · 2020
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 merely monotone (negative) pseudogradient. Furthermore, we show that when the regularizer enjoys strong convexity, the resulting dynamics can converge even in games with hypomonotone (negative) pseudogradient, which corresponds to a shortage of monotonicity.