Diversity-Driven Offline Multi-Objective Optimization via Nested Pareto Set Learning

2026-06-13

AI Summary

This work addresses the challenge of out-of-distribution (OOD) data in offline multi-objective optimization, which often leads surrogate models to generate unrealistic and overly extreme Pareto solutions. To mitigate this issue, the authors propose DOMOO, a novel approach that incorporates cumulative risk control to alleviate OOD effects, jointly optimizes preference and Pareto parameters through nested Pareto set learning, and employs a diversity-driven selection strategy to enhance both solution quality and uniformity. The study also introduces IGD_offline, an innovative evaluation metric tailored for offline settings that balances convergence and diversity. Extensive experiments demonstrate that DOMOO achieves the best average ranking across multiple synthetic and real-world benchmarks, significantly outperforming existing methods.

Abstract

Multi-objective optimization (MOO) has emerged as a powerful approach to solving complex optimization problems involving multiple objectives. In many practical scenarios, function evaluations are unavailable or prohibitively expensive, necessitating optimization solely based on a fixed offline dataset. In this setting, known as offline MOO, the goal is to find out the Pareto set without access to the true objective functions. This setting suffers from the out-of-distribution (OOD) issue, where the surrogate model is not accurate for unseen designs. Due to the OOD issue, surrogate errors may cause the optimizer to select solutions that do not lie on the true Pareto front and are biased toward its extremes. To address this, this paper proposes Diversity-driven Offline Multi-Objective Optimization (DOMOO), which aims to find out a diverse and high-quality set of solutions. First, DOMOO incorporates an accumulative risk control module that estimates the potential risk of candidate solutions and alleviates the OOD issue between the training data and the generated solutions. In addition, a nested Pareto set learning (PSL) strategy is proposed to jointly learn preference and PSL parameters, then optimize them, enabling adaptation to diverse Pareto front geometries. To further enhance solution quality, we design a diversity-driven selection strategy that extracts a representative and well-distributed set of final solutions. To achieve this diversity-driven selection strategy, we propose $\text{IGD}_\text{offline}$, a tailored indicator for the offline setting that considers both diversity and convergence, and avoids the bias of hypervolume indicator. Extensive experiments on synthetic and real-world benchmarks show that DOMOO achieves the best average rank across tasks in both convergence and diversity among the compared methods.

Problem

• offline multi-objective optimization
• out-of-distribution
• Pareto set
• surrogate model
• solution diversity

Innovation

• offline multi-objective optimization
• out-of-distribution (OOD)
• nested Pareto set learning
• diversity-driven selection
• IGD_offline