# GaussianPSL: Soft partitioning for complex PSL problem

arXiv: https://arxiv.org/abs/2509.17889 · HTML: https://mlsanity.com/paper/2509.17889/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 16 of 16)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Efficient Continuous Pareto Exploration in Multi-Task Learning](https://mlsanity.com/paper/2006.16434/) (2020)
- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [Scalable Pareto Front Approximation for Deep Multi-Objective Learning](https://mlsanity.com/paper/2103.13392/) (2021)
- [Pareto Navigation Gradient Descent: a First-Order Algorithm for Optimization in Pareto Set](https://mlsanity.com/paper/2110.08713/) (2021)
- [Evolutionary Preference Sampling for Pareto Set Learning](https://mlsanity.com/paper/2404.08414/) (2024)
- [Improving Pareto Set Learning for Expensive Multi-objective Optimization via Stein Variational Hypernetworks](https://mlsanity.com/paper/2412.17312/) (2024)
- [Multimodal Multi-objective Optimization: Comparative Study of the State-of-the-Art](https://mlsanity.com/paper/2207.04730/) (2022)
- [Optimization over the weakly Pareto set and multi-task learning](https://mlsanity.com/paper/2504.00257/) (2025)
- [Weak Pareto Boundary: The Achilles' Heel of Evolutionary Multi-Objective Optimization](https://mlsanity.com/paper/2505.13854/) (2025)

## Abstract (arXiv)

Many practical applications of multi-objective optimization (MOO), including engineering design, autonomous systems, and machine learning, often yield complex Pareto frontiers (e.g., discontinuous, degenerate, or non-convex), which pose challenges for traditional scalarization and Pareto Set Learning (PSL) methods that struggle to approximate them accurately. In this paper, we propose GaussianPSL, a novel framework that uses soft partitions of the Pareto decision/objective space to address the challenges posed by complex Pareto frontiers. Our method dynamically partitions the space, enabling simple MLP networks to learn localized features within each region and then aggregate this information for the final prediction. This partition-aware strategy enhances both exploration and convergence, reduces sensitivity to initialization, and improves robustness against local optima. Experimental results demonstrate that the proposed approach consistently outperforms standard PSL models in learning complex Pareto fronts while maintaining model simplicity. Overall, GaussianPSL offers a new direction for effective, scalable MOO in challenging frontier geometries.