Simple Extensions of Single-Objective Acquisition Functions and Hedge Strategies for Multi-Objective Bayesian Optimization
Organizations: Department of Aeronautical and Astronautical Engineering University of Southampton Southampton, United Kingdom
Abstract
Multi-objective Bayesian optimization (MOBO) is commonly approached through specialized acquisition functions or scalarization schemes designed to explicitly account for trade-offs among non-preferential objectives. In this work, we show that such complexity might be unnecessary. We propose a framework that extends standard single-objective acquisition functions directly to the multi-objective setting through a hypervolume-based transformation. We further extend hedge strategies for acquisition functions, which are typically used only in single-objective optimization, to the multi-objective regime. Our approach requires minimal modification to existing Bayesian optimization pipelines and avoids the need for bespoke multi-objective formulations. We demonstrate how a broad class of commonly used single-objective acquisition functions and hedge strategies can be adapted in a principled manner to handle multiple objectives, while preserving their intuitive interpretation and computational efficiency. Empirically, we evaluate the proposed methods across a range of synthetic and real-world multi-objective benchmarks. Despite their simplicity, our extensions consistently match or outperform more complex state-of-the-art MOBO methods in terms of optimization performance and sample efficiency. These results suggest that effective multi-objective Bayesian optimization can be achieved by reusing and carefully extending well-established single-objective acquisition strategies, offering a simpler and more flexible alternative to existing approaches.
Figures & tables
| Test Function | q HAX- | q HAX- | q MOJES | q HVKG | q LNParEGO | q LNEHVI |
|---|---|---|---|---|---|---|
| ZDT2 | ||||||
| ZDT4 | ||||||
| ZDT6 | ||||||
| DTLZ1 | ||||||
| DTLZ2 | ||||||
| DTLZ3 |
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
| Test function | Dimensions ( ) | No. of objectives ( ) |
|---|---|---|
| ZDT2 | 9 | 2 |
| ZDT4 | 6 | 2 |
| ZDT6 | 6 | 2 |
| DTLZ1 | 8 | 3 |
| DTLZ2 | 6 | 3 |
| DTLZ3 | 4 | 2 |
| Test Function | q HAX- | q HAX- | q MOJES | q HVKG | q LNParEGO | q LNEHVI |
|---|---|---|---|---|---|---|
| ZDT2 | ||||||
| ZDT4 | ||||||
| ZDT6 | ||||||
| DTLZ1 | ||||||
| DTLZ2 | ||||||
| DTLZ3 |
Bayesian Optimization
Bayesian optimization uses probabilistic models and sequential experiments to find strong solutions when evaluating a black-box objective is costly.
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