# Accelerated Multiple Wasserstein Gradient Flows for Multi-objective Distributional Optimization

arXiv: https://arxiv.org/abs/2601.19220 · HTML: https://mlsanity.com/paper/2601.19220/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [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)
- [A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights](https://mlsanity.com/paper/1503.01243/) (2015)
- [Understanding the Acceleration Phenomenon via High-Resolution Differential Equations](https://mlsanity.com/paper/1810.08907/) (2018)
- [Accelerated Information Gradient flow](https://mlsanity.com/paper/1909.02102/) (2019)
- [Accelerated Flow for Probability Distributions](https://mlsanity.com/paper/1901.03317/) (2019)
- [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)
- [Convergence rates analysis of a multiobjective proximal gradient method](https://mlsanity.com/paper/2010.08217/) (2020)
- [Wasserstein Gradient Flow over Variational Parameter Space for Variational Inference](https://mlsanity.com/paper/2310.16705/) (2023)
- [Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping](https://mlsanity.com/paper/2307.00975/) (2023)
- [Moreau-Yoshida Variational Transport: A General Framework For Solving Regularized Distributional Optimization Problems](https://mlsanity.com/paper/2307.16358/) (2023)
- [Multiple Wasserstein Gradient Descent Algorithm for Multi-Objective Distributional Optimization](https://mlsanity.com/paper/2505.18765/) (2025)

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

- [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 study multi-objective optimization over probability distributions in Wasserstein space. Recently, Nguyen et al. (2025) introduced Multiple Wasserstein Gradient Descent (MWGraD) algorithm, which exploits the geometric structure of Wasserstein space to jointly optimize multiple objectives. Building on this approach, we propose an accelerated variant, A-MWGraD, inspired by Nesterov's acceleration. We analyze the continuous-time dynamics and establish convergence to weakly Pareto optimal points in probability space. Our theoretical results show that A-MWGraD achieves a convergence rate of O(1/t2) for geodesically convex objectives and O(e^-√βt) for β-strongly geodesically convex objectives, improving upon the O(1/t) rate of MWGraD in the geodesically convex setting. We further introduce a practical kernel-based discretization for A-MWGraD and demonstrate through numerical experiments that it consistently outperforms MWGraD in convergence speed and sampling efficiency on multi-target sampling tasks.