Learning Where to Go: Spectrally Aligned Surrogates and Search for Offline Model-Based Optimization

In offline model-based optimization (MBO), the quality of a learned surrogate is determined not only by how well it captures preferences among observed designs, but also by whether its geometry provides reliable directions for optimization beyond the training distribution. Standard learning objectives can preserve useful predictive structure while still admitting high-frequency variations that produce unstable or misleading gradients during out-of-distribution search. We introduce SASS (Spectrally Aligned Surrogates and Search), a framework that aligns surrogate learning and search through a shared spectral inductive bias. SASS trains the surrogate to preserve its induced preferences under high-frequency perturbations, encouraging reliance on stable low-frequency structure while suppressing variations that distort the optimization landscape. At search time, gradient updates are projected onto the same low-frequency subspace, so that surrogate learning and optimization are governed by a common notion of stable structure. Across five Design-Bench tasks, SASS improves over both ranking baselines in mean normalized score on every task. Further analyses assess how spectral projection preserves objective values and rankings, and identify conditions under which the low-frequency assumption breaks down.