# Stochastic Optimization for Regularized Wasserstein Estimators

arXiv: https://arxiv.org/abs/2002.08695 · HTML: https://mlsanity.com/paper/2002.08695/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 9 of 9)

- [Minibatch optimal transport distances; analysis and applications](https://mlsanity.com/paper/2101.01792/) (2021)
- [Doubly Regularized Entropic Wasserstein Barycenters](https://mlsanity.com/paper/2303.11844/) (2023)
- [Hilbert's projective metric for functions of bounded growth and exponential convergence of Sinkhorn's algorithm](https://mlsanity.com/paper/2311.04041/) (2023)
- [Mirror Sinkhorn: Fast Online Optimization on Transport Polytopes](https://mlsanity.com/paper/2211.10420/) (2022)
- [Optimal Transportation by Orthogonal Coupling Dynamics](https://mlsanity.com/paper/2410.08060/) (2024)
- [Distances for Markov chains from sample streams](https://mlsanity.com/paper/2505.18005/) (2025)
- [On the potential benefits of entropic regularization for smoothing Wasserstein estimators](https://mlsanity.com/paper/2210.06934/) (2022)
- [Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterations](https://mlsanity.com/paper/2307.13370/) (2023)
- [Differentiating Bisimulation Metrics: A Framework for Parametric Markov Chain Fitting via Bicausal Optimal Transport](https://mlsanity.com/paper/2609.37239/) (2026)

## Abstract (arXiv)

Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss between distributions that has been used in many applications throughout machine learning and statistics. Recent algorithmic progress on this problem and its regularized versions have made these tools increasingly popular. However, existing techniques require solving an optimization problem to obtain a single gradient of the loss, thus slowing down first-order methods to minimize the sum of losses, that require many such gradient computations. In this work, we introduce an algorithm to solve a regularized version of this problem of Wasserstein estimators, with a time per step which is sublinear in the natural dimensions of the problem. We introduce a dual formulation, and optimize it with stochastic gradient steps that can be computed directly from samples, without solving additional optimization problems at each step. Doing so, the estimation and computation tasks are performed jointly. We show that this algorithm can be extended to other tasks, including estimation of Wasserstein barycenters. We provide theoretical guarantees and illustrate the performance of our algorithm with experiments on synthetic data.