Collaborative Pareto Set Learning in Multiple Multi-Objective Optimization Problems

TL;DR

The paper tackles the inefficiency of learning Pareto sets for multiple MOPs by introducing Collaborative Pareto Set Learning (CoPSL), a neural architecture with shared and MOP-specific layers that learns Pareto sets across $K$ MOPs in a single run. It leverages hard parameter sharing inspired by multi-task learning and employs a Dirichlet-sampled batch of preferences to generate solution sets, optimizing a total loss that aggregates per-MOP objectives with flexible loss variants (LS, COSMOS, TCH, MTCH). Empirical results on synthetic and real-world problems show CoPSL achieves superior efficiency (lower runtime and FLOPs) and robust Pareto set approximation (HV), while revealing that meaningful shareable representations exist among MOPs. The framework demonstrates the potential to exploit cross-MOP relationships to scale Pareto set learning, with avenues for dynamic weighting guided by optimization indicators for further improvements.

Abstract

Pareto Set Learning (PSL) is an emerging research area in multi-objective optimization, focusing on training neural networks to learn the mapping from preference vectors to Pareto optimal solutions. However, existing PSL methods are limited to addressing a single Multi-objective Optimization Problem (MOP) at a time. When faced with multiple MOPs, this limitation results in significant inefficiencies and hinders the ability to exploit potential synergies across varying MOPs. In this paper, we propose a Collaborative Pareto Set Learning (CoPSL) framework, which learns the Pareto sets of multiple MOPs simultaneously in a collaborative manner. CoPSL particularly employs an architecture consisting of shared and MOP-specific layers. The shared layers are designed to capture commonalities among MOPs collaboratively, while the MOP-specific layers tailor these general insights to generate solution sets for individual MOPs. This collaborative approach enables CoPSL to efficiently learn the Pareto sets of multiple MOPs in a single execution while leveraging the potential relationships among various MOPs. To further understand these relationships, we experimentally demonstrate that shareable representations exist among MOPs. Leveraging these shared representations effectively improves the capability to approximate Pareto sets. Extensive experiments underscore the superior efficiency and robustness of CoPSL in approximating Pareto sets compared to state-of-the-art approaches on a variety of synthetic and real-world MOPs. Code is available at https://github.com/ckshang/CoPSL.

Figures (6)

• Figure 1: The fully connected neural network model of collaborative Pareto set learning, which is structured with shared and MOP-specific parameters. This allows it to concurrently learn from multiple MOPs with fewer parameters, enabling more efficient training and inference.
• Figure 2: A toy example to explore mechanisms of the CoPSL model. We train several CoPSL model architectures, each sharing a different number of layers for two MOPs. For each of these models, we plot their performance on each MOP relative to the MOP-specific model. The results demonstrate that the presence of shareable representations for preference vectors is more effectively learned in a collaborative fashion.
• Figure 3: The log HV difference curves of four algorithms for six different problems. The solid line is the mean value averaged over 10 independent runs for each algorithm. The labels of the algorithms can be found in Subfig. (a).
• Figure 4: The log HV difference curves of four algorithms for three problems over 10 independent runs. The labels of the algorithms can be found in Subfig. (a).
• Figure 5: Pareto front comparisons on synthetic benchmark F1. The top part represents PSL, and the bottom part represents CoPSL. Each set of top and bottom comparisons is derived from the same random seed.