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Found 7 papers, 1 papers with code
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.
Multi-index Antithetic Stochastic Gradient Algorithm
In this paper, we construct a Multi-index Antithetic Stochastic Gradient Algorithm (MASGA) whose implementation is independent of the structure of the target measure and which achieves performance on par with Monte Carlo estimators that have access to unbiased samples from the distribution of interest.
Non-asymptotic bounds for sampling algorithms without log-concavity
Finally, we provide a weak convergence analysis that covers both the standard and the randomised (inaccurate) drift case.
Multilevel Monte Carlo methods for the approximation of invariant measures of stochastic differential equations
We show that this is the first stochastic gradient MCMC method with complexity $\mathcal{O}(\varepsilon^{-2}|\log {\varepsilon}|^{3})$, in contrast to the complexity $\mathcal{O}(\varepsilon^{-3})$ of currently available methods.
