Amortized Active Generation of Pareto Sets

Daniel M. Steinberg, Asiri Wijesinghe, Rafael Oliveira, Piotr Koniusz, Cheng Soon Ong, Edwin V. Bonilla

Keywords: multi-objective optimization, multi-objective generation, black-box optimization, guided generation, multi-objective Bayesian optimization, discrete optimization, variational inference, reinforce, active generation, online black-box optimization

TL;DR: We learn a generative model of the Pareto set that can be conditioned on subjective preferences, without retraining, for online multi-objective optimization tasks on discrete/mixed spaces.

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.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 1