7 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…
Almost-sharp convergence rate for the Sinkhorn algorithm in the asymptotically scalable case
Guillaume Wang
We prove that the Sinkhorn algorithm converges at a rate of in -norm marginal error, in the asymptotically scalable case. This almost closes the gap betw…
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…
A higher-order Otto calculus approach to the Gaussian completely monotone conjecture
Guillaume Wang
The Gaussian completely monotone (GCM) conjecture states that the -th time-derivative of the entropy along the heat flow on is positive for even and negative…
An Exponentially Converging Particle Method for the Mixed Nash Equilibrium of Continuous Games
Guillaume Wang, Lénaïc Chizat
We consider the problem of computing mixed Nash equilibria of two-player zero-sum games with continuous sets of pure strategies and with first-order access to the payoff function.…