# Bringing regularized optimal transport to lightspeed: a splitting method adapted for GPUs

arXiv: https://arxiv.org/abs/2305.18483 · HTML: https://mlsanity.com/paper/2305.18483/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 29 May 2023.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Differentiable Ranks and Sorting using Optimal Transport](https://mlsanity.com/paper/1905.11885/) (2019)
- [Understanding and Improving Convolutional Neural Networks via Concatenated Rectified Linear Units](https://mlsanity.com/paper/1603.05201/) (2016)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://mlsanity.com/paper/1610.06519/) (2016)
- [On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms](https://mlsanity.com/paper/1901.06482/) (2019)
- [Sparsity-Constrained Optimal Transport](https://mlsanity.com/paper/2209.15466/) (2022)
- [Quadratically regularized optimal transport](https://mlsanity.com/paper/1903.01112/) (2019)
- [Rethinking Initialization of the Sinkhorn Algorithm](https://mlsanity.com/paper/2206.07630/) (2022)
- [Faster First-Order Primal-Dual Methods for Linear Programming using Restarts and Sharpness](https://mlsanity.com/paper/2105.12715/) (2021)
- [Optimal Transport losses and Sinkhorn algorithm with general convex regularization](https://mlsanity.com/paper/2007.00976/) (2020)
- [A Fast and Accurate Splitting Method for Optimal Transport: Analysis and Implementation](https://mlsanity.com/paper/2110.11738/) (2021)
- [Accelerated Bregman Primal-Dual methods applied to Optimal Transport and Wasserstein Barycenter problems](https://mlsanity.com/paper/2203.00802/) (2022)
- [Trajectory of Alternating Direction Method of Multipliers and Adaptive Acceleration](https://mlsanity.com/paper/1906.10114/) (2019)
- [Gini-regularized Optimal Transport with an Application to Spatio-Temporal Forecasting](https://mlsanity.com/paper/1712.02512/) (2017)
- [Projecting onto rectangular matrices with prescribed row and column sums](https://mlsanity.com/paper/2105.12222/) (2021)

## Built on by (most cited first, 3 of 3)

- [FlashSinkhorn: IO-Aware Entropic Optimal Transport on GPU](https://mlsanity.com/paper/2602.03067/) (2026)
- [cuRegOT: A GPU-Accelerated Solver for Entropic-Regularized Optimal Transport](https://mlsanity.com/paper/2605.08793/) (2026)
- [Annealed Sinkhorn with Momentum: Certified Unregularized Optimal Transport in Linear Memory](https://mlsanity.com/paper/2609.33814/) (2026)

## Abstract (arXiv)

We present an efficient algorithm for regularized optimal transport. In contrast to previous methods, we use the Douglas-Rachford splitting technique to develop an efficient solver that can handle a broad class of regularizers. The algorithm has strong global convergence guarantees, low per-iteration cost, and can exploit GPU parallelization, making it considerably faster than the state-of-the-art for many problems. We illustrate its competitiveness in several applications, including domain adaptation and learning of generative models.