2 citations · 4 across the 10 of their papers we have counts for
10 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…
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.…
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…
Mean-Field Langevin Dynamics for Signed Measures via a Bilevel Approach
Guillaume Wang, Alireza Mousavi-Hosseini, Lénaïc Chizat
Mean-field Langevin dynamics (MLFD) is a class of interacting particle methods that tackle convex optimization over probability measures on a manifold, which are scalable, versatil…
Local Convergence of Gradient Methods for Min-Max Games: Partial Curvature Generically Suffices
Guillaume Wang, Lénaïc Chizat
We study the convergence to local Nash equilibria of gradient methods for two-player zero-sum differentiable games. It is well-known that such dynamics converge locally when $S \su…
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.…
Tight bounds for minimum l1-norm interpolation of noisy data
Guillaume Wang, Konstantin Donhauser, Fanny Yang
We provide matching upper and lower bounds of order for the prediction error of the minimum -norm interpolator, a.k.a. basis pursuit. Our result is tight up…