Amortized Active Generation of Pareto Sets

2025-10-23

AI Summary

Online discrete black-box multi-objective optimization (MOO) faces challenges in Pareto set generation and posterior user preference modeling. Method: We propose an amortized conditional generative framework that (i) implicitly links probabilistic non-dominance estimation to hypervolume improvement—bypassing explicit hypervolume computation; (ii) encodes user-specified trade-off preferences as direction vectors, embedding them into the generator for posterior conditional control; and (iii) employs a class-probability estimator (CPE) to model non-dominance relationships, enabling efficient sampling. Contribution/Results: Our approach generates the complete Pareto front without retraining, substantially improving sample efficiency. It achieves superior preference integration and solution-set quality, as demonstrated on synthetic benchmarks and a real-world protein design task.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning Preferences or Rankings
• Reasoning under Uncertainty: Stochastic Optimization

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
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

We introduce active generation of Pareto sets (A-GPS), a new framework for online discrete black-box multi-objective optimization (MOO). A-GPS learns a generative model of the Pareto set that supports a-posteriori conditioning on user preferences. The method employs a class probability estimator (CPE) to predict non-dominance relations and to condition the generative model toward high-performing regions of the search space. We also show that this non-dominance CPE implicitly estimates the probability of hypervolume improvement (PHVI). To incorporate subjective trade-offs, A-GPS introduces preference direction vectors that encode user-specified preferences in objective space. At each iteration, the model is updated using both Pareto membership and alignment with these preference directions, producing an amortized generative model capable of sampling across the Pareto front without retraining. The result is a simple yet powerful approach that achieves high-quality Pareto set approximations, avoids explicit hypervolume computation, and flexibly captures user preferences. Empirical results on synthetic benchmarks and protein design tasks demonstrate strong sample efficiency and effective preference incorporation.

Problem

• Online discrete black-box multi-objective optimization framework
• Generative modeling of Pareto sets with user preferences
• Avoids explicit hypervolume computation while capturing preferences

Innovation

• Generative model learns Pareto set distributions
• Class probability estimator predicts non-dominance relations
• Preference vectors enable amortized sampling without retraining