Amortized Active Generation of Pareto Sets

TL;DR

This paper presents A-GPS, a novel framework for efficiently generating Pareto sets in multi-objective optimization by learning a generative model that incorporates user preferences and non-dominance predictions.

Contribution

A-GPS introduces a generative modeling approach for Pareto sets that supports online updates, preference conditioning, and avoids explicit hypervolume calculations.

Findings

Achieves high-quality Pareto set approximations.

Demonstrates strong sample efficiency on benchmarks.

Effectively incorporates subjective user preferences.

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.