# Multi-Objective Optimization via Wasserstein-Fisher-Rao Gradient Flow

arXiv: https://arxiv.org/abs/2311.13159 · HTML: https://mlsanity.com/paper/2311.13159/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 61 references that are in the map.
- First posted on arXiv 22 Nov 2023.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [Introducing LETOR 4.0 Datasets](https://mlsanity.com/paper/1306.2597/) (2013)
- [A Theoretical Analysis of NDCG Type Ranking Measures](https://mlsanity.com/paper/1304.6480/) (2013)
- [Controllable Pareto Multi-Task Learning](https://mlsanity.com/paper/2010.06313/) (2020)
- [The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning](https://mlsanity.com/paper/1907.04472/) (2019)
- [Accelerating Langevin Sampling with Birth-death](https://mlsanity.com/paper/1905.09863/) (2019)
- [Scalable Pareto Front Approximation for Deep Multi-Objective Learning](https://mlsanity.com/paper/2103.13392/) (2021)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Uncertainty-Aware Search Framework for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2204.05944/) (2022)
- [Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics](https://mlsanity.com/paper/2211.00450/) (2022)
- [Learning Gaussian Mixtures Using the Wasserstein-Fisher-Rao Gradient Flow](https://mlsanity.com/paper/2301.01766/) (2023)
- [Improving Pareto Front Learning via Multi-Sample Hypernetworks](https://mlsanity.com/paper/2212.01130/) (2022)
- [Multi-Label Learning to Rank through Multi-Objective Optimization](https://mlsanity.com/paper/2207.03060/) (2022)
- [Multi-task problems are not multi-objective](https://mlsanity.com/paper/2110.07301/) (2021)

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

- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion](https://mlsanity.com/paper/2509.25171/) (2025)
- [COS-DPO: Conditioned One-Shot Multi-Objective Fine-Tuning Framework](https://mlsanity.com/paper/2410.08316/) (2024)

## Abstract (arXiv)

Multi-objective optimization (MOO) aims to optimize multiple, possibly conflicting objectives with widespread applications. We introduce a novel interacting particle method for MOO inspired by molecular dynamics simulations. Our approach combines overdamped Langevin and birth-death dynamics, incorporating a "dominance potential" to steer particles toward global Pareto optimality. In contrast to previous methods, our method is able to relocate dominated particles, making it particularly adept at managing Pareto fronts of complicated geometries. Our method is also theoretically grounded as a Wasserstein-Fisher-Rao gradient flow with convergence guarantees. Extensive experiments confirm that our approach outperforms state-of-the-art methods on challenging synthetic and real-world datasets.