# Sparse Partial Optimal Transport via Quadratic Regularization

arXiv: https://arxiv.org/abs/2508.08476 · HTML: https://mlsanity.com/paper/2508.08476/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 66 references that are in the map.
- First posted on arXiv 11 Aug 2025.

## Builds on (most cited first, 27 of 27)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [SGD and Hogwild! Convergence Without the Bounded Gradients Assumption](https://mlsanity.com/paper/1802.03801/) (2018)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [Optimal Transport for Multi-source Domain Adaptation under Target Shift](https://mlsanity.com/paper/1803.04899/) (2018)
- [Clarabel: An interior-point solver for conic programs with quadratic objectives](https://mlsanity.com/paper/2405.12762/) (2024)
- [From optimal transport to generative modeling: the VEGAN cookbook](https://mlsanity.com/paper/1705.07642/) (2017)
- [On the Efficiency of Entropic Regularized Algorithms for Optimal Transport](https://mlsanity.com/paper/1906.01437/) (2019)
- [Sparsity-Constrained Optimal Transport](https://mlsanity.com/paper/2209.15466/) (2022)
- [Unpaired Deep Learning for Accelerated MRI using Optimal Transport Driven CycleGAN](https://mlsanity.com/paper/2008.12967/) (2020)
- [Fast Optimal Transport Averaging of Neuroimaging Data](https://mlsanity.com/paper/1503.08596/) (2015)
- [Globally Convergent Type-I Anderson Acceleration for Non-Smooth Fixed-Point Iterations](https://mlsanity.com/paper/1808.03971/) (2018)
- [Optimal Transport for Conditional Domain Matching and Label Shift](https://mlsanity.com/paper/2006.08161/) (2020)
- [On Unbalanced Optimal Transport: Gradient Methods, Sparsity and Approximation Error](https://mlsanity.com/paper/2202.03618/) (2022)
- [Tsallis Regularized Optimal Transport and Ecological Inference](https://mlsanity.com/paper/1609.04495/) (2016)
- [Quadratically regularized optimal transport](https://mlsanity.com/paper/1903.01112/) (2019)
- [Primal-dual accelerated gradient methods with small-dimensional relaxation oracle](https://mlsanity.com/paper/1809.05895/) (2018)
- [Decentralized Frank-Wolfe Algorithm for Convex and Non-convex Problems](https://mlsanity.com/paper/1612.01216/) (2016)
- [Entropic regularization of continuous optimal transport problems](https://mlsanity.com/paper/1906.01333/) (2019)
- [On Partial Optimal Transport: Revising the Infeasibility of Sinkhorn and Efficient Gradient Methods](https://mlsanity.com/paper/2312.13970/) (2023)
- [Correlated Attention in Transformers for Multivariate Time Series](https://mlsanity.com/paper/2311.11959/) (2023)
- [Quadratically Regularized Optimal Transport: Existence and Multiplicity of Potentials](https://mlsanity.com/paper/2404.06847/) (2024)
- [Understanding the Scalability of Hyperledger Fabric](https://mlsanity.com/paper/2107.09886/) (2021)
- [Stochastic Constrained Decentralized Optimization for Machine Learning with Fewer Data Oracles: a Gradient Sliding Approach](https://mlsanity.com/paper/2404.02511/) (2024)
- [Coded Computing for Fault-Tolerant Parallel QR Decomposition](https://mlsanity.com/paper/2311.11943/) (2023)

## Built on by (most cited first, 1 of 1)

- [Accelerated Algorithm for Sparse Regularized Partial Optimal Transport](https://mlsanity.com/paper/2609.40075/) (2026)

## Abstract (arXiv)

Partial Optimal Transport (POT) has recently emerged as a central tool in various Machine Learning (ML) applications. It lifts the stringent assumption of the conventional Optimal Transport (OT) that input measures are of equal masses, which is often not guaranteed in real-world datasets, and thus offers greater flexibility by permitting transport between unbalanced input measures. Nevertheless, existing major solvers for POT commonly rely on entropic regularization for acceleration and thus return dense transport plans, hindering the adoption of POT in various applications that favor sparsity. In this paper, as an alternative approach to the entropic POT formulation in the literature, we propose a novel formulation of POT with quadratic regularization, hence termed quadratic regularized POT (QPOT), which induces sparsity to the transport plan and consequently facilitates the adoption of POT in many applications with sparsity requirements. Extensive experiments on synthetic and CIFAR-10 datasets, as well as real-world applications such as color transfer and domain adaptations, consistently demonstrate the improved sparsity and favorable performance of our proposed QPOT formulation.