Amortized Multi-Objective Optimization Across Tasks with Generative Solution Modeling

TL;DR

This paper introduces a generative, inverse modeling approach to efficiently solve families of expensive multi-objective optimization problems across varying tasks without re-evaluations.

Contribution

It proposes a novel parametric Bayesian optimizer that learns to predict solutions directly for any task in the continuous parameter space, reducing computational costs.

Findings

The method achieves faster convergence by leveraging inter-task synergies.

Empirical results verify effectiveness on synthetic and real-world benchmarks.

The approach enables direct solution prediction for unseen tasks without re-evaluation.

Abstract

Many real-world applications require solving families of expensive multi-objective optimization problems~(EMOPs) under varying operational conditions. This can be formulated as parametric expensive multi-objective optimization problems (P-EMOPs) where each task parameter defines a distinct optimization instance. Current multi-objective Bayesian optimization methods have been widely used for finding finite sets of Pareto optimal solutions for each task. However, P-EMOPs present a fundamental challenge: the continuous task parameter space can contain infinite distinct problems, each requiring separate expensive evaluations. To address this, we propose learning an inverse model to amortize the multi-objective optimization cost across the continuous task-preference space, enabling direct solution prediction for any query without the need for expensive re-evaluation. This paper introduces a novel parametric multi-objective Bayesian optimizer that learns this inverse model by alternating between (1) generative solution sampling via conditional generative models and (2) acquisition-driven search leveraging inter-task synergies. This approach enables effective optimization across multiple tasks and finally achieves direct solution prediction for unseen parameterized EMOPs without re-evaluations. We theoretically justify the faster convergence by leveraging inter-task synergies through task-aware Gaussian processes. Based on that, empirical studies in synthetic and real-world benchmarks further verify the effectiveness of the proposed parametric optimizer.