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Statistical Rates for Entropic Optimal Transport in the Discrete to SubGaussian Regime

arXiv · AI, language, vision and robotics · article · Sep 22, 2026 · UTC

We study statistical rates in entropic optimal transport in the semi-discrete regime where one measure has finite support and the other is subGaussian. Our main result establishes parametric convergence rates for the empirical dual potentials to their population counterparts, with no dimension dependence in the leading term. Our result relies on tailored strong concavity analysis of the semi-dual objective, coupled with specialized bounds for the semi-discrete potentials. As a consequence, we obtain fast rates for downstream quantities derived from the optimal coupling. Chiefly, the empirical

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