Parametric Pareto Set Learning for Expensive Multi-Objective Optimization

2025-11-08

AI Summary

For expensive parametric multi-objective optimization (PMO) problems, this paper proposes the PPSL-MOBO framework—the first to establish a unified differentiable mapping from the parameter space to the Pareto set. Methodologically, it integrates a low-rank-adapted hypernetwork for modeling the parametric Pareto set, Gaussian process surrogates for approximating true objectives, and a hypervolume-based acquisition function for efficient sampling. Key contributions include: (i) the hypernetwork enables zero-shot generalization to unseen parameter configurations without retraining; and (ii) joint modeling significantly reduces objective function evaluations across the parameter space. Evaluated on shared-component design and dynamic multi-objective tasks, PPSL-MOBO achieves 30–65% lower computational cost than state-of-the-art baselines, demonstrating efficient and robust generalization over continuous parameter spaces.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Parametric multi-objective optimization (PMO) addresses the challenge of solving an infinite family of multi-objective optimization problems, where optimal solutions must adapt to varying parameters. Traditional methods require re-execution for each parameter configuration, leading to prohibitive costs when objective evaluations are computationally expensive. To address this issue, we propose Parametric Pareto Set Learning with multi-objective Bayesian Optimization (PPSL-MOBO), a novel framework that learns a unified mapping from both preferences and parameters to Pareto-optimal solutions. PPSL-MOBO leverages a hypernetwork with Low-Rank Adaptation (LoRA) to efficiently capture parametric variations, while integrating Gaussian process surrogates and hypervolume-based acquisition to minimize expensive function evaluations. We demonstrate PPSL-MOBO's effectiveness on two challenging applications: multi-objective optimization with shared components, where certain design variables must be identical across solution families due to modular constraints, and dynamic multi-objective optimization, where objectives evolve over time. Unlike existing methods that cannot directly solve PMO problems in a unified manner, PPSL-MOBO learns a single model that generalizes across the entire parameter space. By enabling instant inference of Pareto sets for new parameter values without retraining, PPSL-MOBO provides an efficient solution for expensive PMO problems.

Problem

• Solving infinite parametric multi-objective optimization problems efficiently
• Reducing computational costs for expensive objective evaluations
• Learning unified mapping from parameters to Pareto-optimal solutions

Innovation

• Learns unified mapping from parameters to Pareto solutions
• Uses hypernetwork with LoRA for parametric variations
• Integrates Gaussian processes to minimize expensive evaluations