GaussianPSL: A novel framework based on Gaussian Splatting for exploring the Pareto frontier in multi-criteria optimization

Abstract: Multi-objective optimization (MOO) is essential for solving complex real-world problems involving multiple conflicting objectives. However, many practical applications - including engineering design, autonomous systems, and machine learning - often yield non-convex, degenerate, or discontinuous Pareto frontiers, which involve traditional scalarization and Pareto Set Learning (PSL) methods that struggle to approximate accurately. Existing PSL approaches perform well on convex fronts but tend to fail in capturing the diversity and structure of irregular Pareto sets commonly observed in real-world scenarios. In this paper, we propose Gaussian-PSL, a novel framework that integrates Gaussian Splatting into PSL to address the challenges posed by non-convex Pareto frontiers. Our method dynamically partitions the preference vector space, enabling simple MLP networks to learn localized features within each region, which are then integrated by an additional MLP aggregator. This partition-aware strategy enhances both exploration and convergence, reduces sensi- tivity to initialization, and improves robustness against local optima. We first provide the mathematical formulation for controllable Pareto set learning using Gaussian Splat- ting. Then, we introduce the Gaussian-PSL architecture and evaluate its performance on synthetic and real-world multi-objective benchmarks. Experimental results demonstrate that our approach outperforms standard PSL models in learning irregular Pareto fronts while maintaining computational efficiency and model simplicity. This work offers a new direction for effective and scalable MOO under challenging frontier geometries.