# Multiple Wasserstein Gradient Descent Algorithm for Multi-Objective Distributional Optimization

arXiv: https://arxiv.org/abs/2505.18765 · HTML: https://mlsanity.com/paper/2505.18765/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 24 May 2025.

## Builds on (most cited first, 17 of 17)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropout](https://mlsanity.com/paper/2010.06808/) (2020)
- [First-order Methods for Geodesically Convex Optimization](https://mlsanity.com/paper/1602.06053/) (2016)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [A Unified Particle-Optimization Framework for Scalable Bayesian Sampling](https://mlsanity.com/paper/1805.11659/) (2018)
- [Multi-Objective SPIBB: Seldonian Offline Policy Improvement with Safety Constraints in Finite MDPs](https://mlsanity.com/paper/2106.00099/) (2021)
- [Stochastic Multiple Target Sampling Gradient Descent](https://mlsanity.com/paper/2206.01934/) (2022)
- [On a linear fused Gromov-Wasserstein distance for graph structured data](https://mlsanity.com/paper/2203.04711/) (2022)
- [Learning subtree pattern importance for Weisfeiler-Lehmanbased graph kernels](https://mlsanity.com/paper/2106.04739/) (2021)
- [Wasserstein Gradient Flow over Variational Parameter Space for Variational Inference](https://mlsanity.com/paper/2310.16705/) (2023)
- [Moreau-Yoshida Variational Transport: A General Framework For Solving Regularized Distributional Optimization Problems](https://mlsanity.com/paper/2307.16358/) (2023)
- [Particle Optimization in Stochastic Gradient MCMC](https://mlsanity.com/paper/1711.10927/) (2017)

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

- [Accelerated Multiple Wasserstein Gradient Flows for Multi-objective Distributional Optimization](https://mlsanity.com/paper/2601.19220/) (2026)
- [Structured Credal Learning](https://mlsanity.com/paper/2603.14070/) (2026)
- [Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors](https://mlsanity.com/paper/2610.10187/) (2026)

## Abstract (arXiv)

We address the optimization problem of simultaneously minimizing multiple objective functionals over a family of probability distributions. This type of Multi-Objective Distributional Optimization commonly arises in machine learning and statistics, with applications in areas such as multiple target sampling, multi-task learning, and multi-objective generative modeling. To solve this problem, we propose an iterative particle-based algorithm, which we call Muliple Wasserstein Gradient Descent (MWGraD), which constructs a flow of intermediate empirical distributions, each being represented by a set of particles, which gradually minimize the multiple objective functionals simultaneously. Specifically, MWGraD consists of two key steps at each iteration. First, it estimates the Wasserstein gradient for each objective functional based on the current particles. Then, it aggregates these gradients into a single Wasserstein gradient using dynamically adjusted weights and updates the particles accordingly. In addition, we provide theoretical analysis and present experimental results on both synthetic and real-world datasets, demonstrating the effectiveness of MWGraD.