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SMOG: Scalable Meta-Learning 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 SMOG, a scalable multi-output GP meta-learning surrogate for multi-objective Bayesian optimization that learns cross-objective correlations and propagates meta-task uncertainty into a closed-form target prior.

Problem

Meta-learning for expensive multi-objective black-box optimization in the low-data regime, where existing methods either do not scale across many meta-tasks, treat objectives independently, or lack principled uncertainty propagation.

Approach

A structured multi-output GP prior across meta- and target tasks, with per-objective meta-task weights w_mo so that conditioning on metadata yields a closed-form target prior whose covariance couples objectives via w_mo w_mo', plus an equicorrelated residual kernel for target objectives; cost scales linearly in number of meta-tasks and reduces to ScaML-GP for single objective.

Key results

• SMOG attains the lowest or near-lowest cumulative HV regret on all four synthetic configurations (BraninCurrin and Hartmann6, 2 and 4 objectives), while MO-GP and Ind. GP accumulate the highest regret.
• On the terrain benchmark, SMOG's advantage grows from 2 to 4 objectives, with a wide gap to other methods on the 4-objective variant of target task 0.
• Per BO loop runtime on Hartmann6 is about 6.4 s for 2 objectives and about 16.8 s for 4 objectives.

Surprising findings

• Ind. ABLR and Ind. SGPT occasionally outperform SMOG on individual HPOBench and terrain problems, though they struggle on others.

Limitations

• Each task GP is exact and scales cubically with data points, so large datasets need sparse or approximate GPs.
• Assumes all tasks share the same search and objective spaces.
• Two-stage hyperparameter optimization without target-to-meta feedback; meta-task correlations ignored by design.

Experimental setup

Datasets: Hartmann6 (adapted) Branin-Currin (adapted) HPOBench (Slice Localization, Protein Structure, Naval Propulsion, Parkinson's Telemonitoring) Terrain benchmark (MetaBox)

Benchmarks: Hartmann6 (2 and 4 obj) Branin-Currin (2 and 4 obj) HPOBench (4 datasets) Terrain (2 and 4 obj)

Metrics: cumulative hypervolume regret hypervolume gap wall-clock runtime NLPD RMSE

Baselines: MO-GP Ind. GP Ind. ScaML-GP MO-TPE Ind. RGPE Ind. SGPT Ind. ABLR Ind. GC3P Ind. SMOG

Builds on: ScaML-GP multi-task GP RGPE LogEHVI

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