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arXiv · 2208.14391

Convergence Rates for Regularized Optimal Transport via Quantization

Stephan Eckstein·Marcel Nutz
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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 multi-marginal problems are obtained. A novel methodology using quantization and martingale couplings is suitable for non-compact marginals and achieves, in particular, the sharp leading-order term of entropically regularized 2-Wasserstein distance for all marginals with finite $(2+\delta)$-moment.

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Stephan Eckstein, Marcel Nutz. 2022-08-30. Convergence Rates for Regularized Optimal Transport via Quantization. https://arxiv.org/abs/2208.14391

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