Mixture-Model Preference Learning for Many-Objective Bayesian Optimization

arXiv stat.ML / 3/31/2026

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Key Points

The paper addresses preference-based many-objective Bayesian optimization challenges caused by a growing trade-off space and human value structures that vary by context.
It introduces a Bayesian framework that learns a small set of latent “preference archetypes” using a Dirichlet-process mixture, capturing uncertainty over both which archetypes apply and how strongly they are weighted.
For efficient optimization queries, it proposes hybrid query strategies that separately target (i) identifying the most relevant mode/archetype and (ii) resolving trade-offs within that mode.
The authors provide a regret guarantee under mild assumptions for their mixture-aware Bayesian optimization procedure.
Experiments on synthetic and real-world benchmarks show improved performance over standard baselines, and diagnostic tools uncover structure that regret metrics alone miss.

Abstract

Preference-based many-objective optimization faces two obstacles: an expanding space of trade-offs and heterogeneous, context-dependent human value structures. Towards this, we propose a Bayesian framework that learns a small set of latent preference archetypes rather than assuming a single fixed utility function, modelling them as components of a Dirichlet-process mixture with uncertainty over both archetypes and their weights. To query efficiently, we designing hybrid queries that target information about (i) mode identity and (ii) within-mode trade-offs. Under mild assumptions, we provide a simple regret guarantee for the resulting mixture-aware Bayesian optimization procedure. Empirically, our method outperforms standard baselines on synthetic and real-world many-objective benchmarks, and mixture-aware diagnostics reveal structure that regret alone fails to capture.