Conservative Pareto Set Amortization for Offline Multi-Objective Optimization

Offline multi-objective optimization aims to identify high-quality trade-off designs using only a fixed dataset of previously evaluated candidates. Existing methods often cast this problem as guided generative sampling, producing a finite candidate pool by steering a diffusion or flow model toward Pareto-preferred regions. We study a different interface: deterministic Pareto set amortization. Our method, Offline Pareto Set Learning (OffPSL), trains a preference-conditioned map $h_\pi:\Delta^{m-1}\rightarrow \mathcal{X}$ that returns one design for each requested trade-off direction. Because offline data contain no preference–solution labels, OffPSL trains this map using two offline-only signals: a coordinate-wise pessimistic surrogate scalarization and a diffusion-style denoising-residual support regularizer learned from offline designs. The denoising model is used only as a frozen support prior and is not used to sample candidates. At inference, OffPSL produces exactly one candidate per reference direction with no iterative sampling, test-time optimization, or filtering from a larger generated pool. On standard offline MOO benchmarks, OffPSL is competitive with recent guided generative baselines while keeping the learned preference-to-design map directly queryable and diagnosable.