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Simple Extensions of Single-Objective Acquisition Functions and Hedge Strategies for Multi-Objective Bayesian Optimization

NeurIPS 2026 · Probabilistic and scientific modeling › Bayesian optimization · approach: Multi-objective Bayesian optimization · 0 citations (OpenAlex)

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Proposes qHAX-α, which wraps standard single-objective acquisitions (UCB, EI) in a Pareto candidate set ranked by posterior-mean hypervolume, and MO-Hedge, a multi-objective GP-Hedge portfolio, evaluated against state-of-the-art MOBO baselines on nine benchmarks.

Problem

Multi-objective Bayesian optimization under small evaluation budgets: approximating the Pareto front with sample-efficient acquisition strategies, where specialized MO acquisitions are complex and no single acquisition dominates.

Approach

Reuse single-objective acquisitions per objective to form a vector acquisition, generate a Pareto-diverse candidate set via NSGA-II, and select batch points greedily by hypervolume of posterior-mean Pareto front; additionally extend GP-Hedge to select among acquisitions using hypervolume-based gains.

Key results

• qHAX-UCB shows strong and consistent performance across all nine benchmarks, achieving best or near-best final hypervolume gap on several tasks (batch Q=3, 20 runs).
• qHAX-α runtime is roughly 230 s per run (Q=3) versus about 2800-8100 s for qMOJES on several benchmarks, per the reported tables.
• MO-Hedge variants track their strongest constituent acquisition across benchmarks, showing robustness to acquisition mismatch.

Surprising findings

• The authors found empirically that a recalibrated-gains hedge variant outperforms the theoretically bounded frozen-reward variant, despite lacking the regret guarantee.

Limitations

• Relies on an inner NSGA-II Pareto optimization that is evolutionary and does not exploit gradients.
• The hypervolume submodularity guarantee is myopic and per-iteration only.
• The recalibrated-gains MO-Hedge lacks the theoretical regret bound of the standard Hedge analysis.

Experimental setup

Datasets: ZDT2 ZDT4 ZDT6 DTLZ1 DTLZ2 DTLZ3 Branin-Currin Welded Beam Vehicle Crash Safety

Benchmarks: ZDT2 ZDT4 ZDT6 DTLZ1 DTLZ2 DTLZ3 Branin-Currin Welded Beam Vehicle Crash Safety

Metrics: log-normalized hypervolume gap log-normalized IGD gap wall-clock runtime

Baselines: qLNEHVI qLNParEGO qHVKG qLB-MOJES

Builds on: GP-Hedge ParEGO EHVI qNEHVI HVKG MOJES

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