4 papers
Effective dynamics of the Sinkhorn algorithm in the regime of low entropy regularization
Guillaume Wang
The Sinkhorn algorithm is the de facto standard method for numerically solving entropy-regularized optimal transport problems over finite sets. In this work, we investigate a pheno…
Sharp convergence rate for the Sinkhorn algorithm via a local analysis
Guillaume Wang
We prove that the Sinkhorn algorithm converges at the rate of in -norm marginal error and in joint relative entropy, which is known to be sharp in the asymptotical…
Local convergence of mean-field Langevin dynamics: from gradient flows to linearly monotone games
Guillaume Wang, Lénaïc Chizat
We study the local convergence of diffusive mean-field systems, including Wasserstein gradient flows, min-max dynamics, and multi-species games. We establish exponential local conv…
The entropy power conjecture implies the McKean conjecture
Guillaume Wang
After reviewing the entropy power, the McKean, and the Gaussian completely monotone conjectures, we prove that the first implies the second, for each order of the time-derivative.…