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Non-convex entropic mean-field optimization via Best Response flow
We study the problem of minimizing non-convex functionals on the space of probability measures, regularized by the relative entropy (KL divergence) with respect to a fixed reference measure, as well as the corresponding problem of solving entropy-regularized non-convex-non-concave min-max problems.
Linear convergence of proximal descent schemes on the Wasserstein space
Since the relative entropy is not Wasserstein differentiable, we prove that along the scheme the iterates belong to a certain class of Sobolev regularity, and hence the relative entropy $\operatorname{KL}(\cdot|\pi)$ has a unique Wasserstein sub-gradient, and that the relative Fisher information is indeed finite.
A Fisher-Rao gradient flow for entropic mean-field min-max games
Gradient flows play a substantial role in addressing many machine learning problems.
Mirror Descent-Ascent for mean-field min-max problems
We study two variants of the mirror descent-ascent algorithm for solving min-max problems on the space of measures: simultaneous and sequential.
