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Bayesian Optimization for Unknown Cost-Varying Variable Subsets with No-Regret Costs
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Extends Bayesian optimization with cost-varying variable subsets (BOCVS) to random, unknown subset costs and proposes an explore-then-commit GP-UCB algorithm with sublinear quality and cost regret.
Problem
Bayesian optimization where controlling certain query variables costs money and the per-subset costs are unknown and random, so the learner must trade off informative control subsets against cheap randomly sampled ones.
Approach
Explore-then-commit algorithm that first filters out low-quality control subsets using intersected GP confidence bounds (tolerance alpha), then in exploitation picks the cheapest high-quality subset using a cost LCB estimated from observed random costs; introduces quality and cost regret definitions.
Key results
- Proposed method outperforms UCB-PSQ, TS-PSQ and ETC-50 in simple regret against cost spent across synthetic and real-world objectives (5 seeds).
- Theory: with high probability, quality regret and cost regret are sublinear in T under suitable exploration length tau.
- Proposed method performs significantly more evaluations once exploitation starts, by favoring cheap valid subsets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the proposed cost-sensitive explore-then-commit algorithm instead of the baseline methods | Bayesian Optimization with cost-varying variable subsets · Hartmann, Ackley, plant growth, and airfoil self-noise benchmarks | simple regret | Helped |
| prioritize cost-effective feasible subsets during exploitation | proposed method · BOCVS benchmarks | evaluations per cost spent | Helped |
Limitations
- Relies on a fixed, known alpha and an exploration length tau requiring knowledge of gap epsilon and horizon T in theory.
- Experiments use only small numbers of control sets and a 100-unit budget with 5 seeds.
- Cost distributions in experiments are synthetic (fixed means with added Gaussian noise).
Experimental setup
Datasets: Hartmann (6-D) synthetic Ackley (6-D) synthetic Plant growth simulator built from Marchantia leaf-area data Airfoil self-noise dataset (UCI)
Benchmarks: Hartmann Ackley plant growth simulator airfoil self-noise
Metrics: simple regret vs cost spent number of evaluations vs cost spent
Baselines: UCB-PSQ TS-PSQ ETC-50 (UCB-CVS variant)
Builds on: UCB-CVS BOPSQ GP-UCB Bayesian optimization with cost-varying variable subsets
Closest papers by meaning
- BONSAI: Bayesian Optimization with Natural Simplicity and Interpretability (NeurIPS 2026 · similarity 0.89)
- Bayesian Optimisation with Unknown Hyperparameters: Regret Bounds Logarithmically Closer to Optimal (NeurIPS 2024 · similarity 0.89)
- Cost-aware Bayesian Optimization via the Pandora's Box Gittins Index (NeurIPS 2024 · similarity 0.87)
- Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation (AAAI 2024 · similarity 0.87)
- BayeSQP: Bayesian Optimization through Sequential Quadratic Programming (NeurIPS 2025 · similarity 0.87)
- Batched Energy-Entropy acquisition for Bayesian Optimization (NeurIPS 2024 · similarity 0.87)
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