Convergence Rates for Regularized Optimal Transport via Quantization
Stephan Eckstein, Marcel Nutz
Abstract
We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. Sharp rates for general divergences including relative entropy or L p regularization, general transport costs, and multimarginal problems are obtained. A novel methodology using quantization and martingale couplings is suitable for noncompact marginals and achieves, in particular, the sharp leading-order term of entropically regularized 2-Wasserstein distance for marginals with a finite [Formula: see text]-moment. Funding: This work was supported by the Alfred P. Sloan Foundation [Grant FG-2016-6282] and the Division of Mathematical Sciences [Grants DMS-1812661 and DMS-2106056].
Topics & Concepts
MathematicsRegularization (linguistics)Kullback–Leibler divergenceApplied mathematicsRate of convergenceMartingale (probability theory)Weak convergenceEntropy (arrow of time)Mathematical optimizationStatisticsComputer sciencePhysicsComputer securityComputer networkChannel (broadcasting)Artificial intelligenceQuantum mechanicsAsset (computer security)Geometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsMarkov Chains and Monte Carlo Methods