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

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.

When designing a drug molecule or a neural network, engineers must balance multiple conflicting goals, for instance, high efficacy versus low toxicity. In practice, testing each candidate design is extremely expensive, so we can only use historical data from past experiments. The challenge is that models trained on this limited data become unreliable when evaluating new, untested designs; they tend to make overly optimistic predictions about regions far from the training data. This causes optimization algorithms to pick "fake winners" that look good on paper but fail in reality, while many genuinely promising designs get overlooked. We developed DOMOO, a method that learns to generate diverse and reliable candidate designs from historical data alone, without new experiments. DOMOO first trains an "energy model" that flags how risky each design is, like a quality inspector on an assembly line. It then learns to map different trade-off preferences (e.g., "efficacy matters more than toxicity") to specific designs, while using the risk signal to steer away from unreliable regions. Finally, it selects a well-spread set of candidates, ensuring diverse options rather than a cluster of similar-looking ones. Across 40+ benchmark tasks spanning molecular design, robotics control, and neural architecture search, DOMOO achieves the best overall ranking compared to existing methods. By explicitly avoiding unreliable predictions, our method produces solutions that are not only diverse but also trustworthy, reducing the chance that a recommended design fails in the real world. This work highlights the importance of risk awareness in data-driven optimization for domains where every experiment counts.