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A General Framework for User-Guided Bayesian Optimization
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Proposes ColaBO, a Bayesian-principled framework that injects user beliefs over the optimum, optimal value, or preferences into a GP surrogate via a belief-weighted prior, applicable to Monte Carlo acquisition functions.
Problem
Standard Bayesian optimization only encodes prior beliefs through GP kernels and hyperparameters, so practitioners cannot inject richer knowledge such as the likely location of the optimum or the optimal value, which limits efficiency under tight budgets.
Approach
Reweights GP prior samples by a user belief over function properties (rejection sampling on draws from the RFF-based decoupled prior), yielding a belief-weighted posterior on which Monte Carlo acquisition functions (LogEI, MES) are computed; this acts on the surrogate in a Bayesian way rather than as a heuristic.
Key results
- With well-located priors, ColaBO-LogEI and ColaBO-MES offer drastic speed-ups over vanilla variants on synthetic functions, comparable to piBO.
- On poorly located priors, ColaBO recovers vanilla acquisition performance within 20D iterations, while piBO is more frequently misled.
- On PD1 tasks, ColaBO variants give the best terminal performance on two of three tasks and reach baseline terminal performance within a third of the budget on CIFAR and LM1B.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ColaBO with a well-located prior over the optimum | ColaBO versus vanilla LogEI and MES · Synthetic functions | optimization performance | Helped |
| Use ColaBO with a poorly located prior over the optimum | ColaBO versus vanilla acquisition functions and πBO · Synthetic functions | optimization performance | Mixed |
| Use ColaBO-LogEI with a poorly located prior | ColaBO-LogEI · Hartmann (6D) | optimization performance | Hurt |
| Use ColaBO-MES with a poorly located prior | ColaBO-MES · Synthetic functions | optimization performance | No clear effect |
| Use ColaBO with priors over the optimal value | ColaBO versus baselines · Synthetic functions | optimization efficiency | Helped |
| Use an accurate prior over the optimal value | ColaBO on Hartmann (6D) · Hartmann (6D) | terminal optimization performance | Helped |
| Use ColaBO with MF-Prior-Bench priors | ColaBO-LogEI versus non-prior baselines · LCBench deep-learning HPO tasks | optimization performance | Mixed |
| Use πBO instead of ColaBO on LCBench | πBO versus ColaBO · LCBench deep-learning HPO tasks | aggregate optimization performance | Helped |
| Use ColaBO with MF-Prior-Bench priors | ColaBO versus vanilla counterparts · PD1 hyperparameter-tuning tasks | optimization speed | Helped |
| Use ColaBO on PD1 | ColaBO versus other methods · PD1 CIFAR and LM1B | terminal performance | Helped |
| Use ColaBO with a Matérn-5/2 kernel instead of a squared-exponential kernel (ablation) | ColaBO · Synthetic functions | aggregate optimization performance | Hurt |
| Use ColaBO-LogEI on Hartmann (6D) with a Matérn-5/2 kernel (ablation) | ColaBO-LogEI · Hartmann (6D) | optimization performance | Hurt |
Surprising findings
- On LCBench, piBO performs best on aggregate, ahead of ColaBO-LogEI.
- The RFF-based approximation bias makes ColaBO struggle with Matern-5/2 kernels, where it is marginally worse on aggregate.
Limitations
- Computationally expensive, requiring multiple MC steps and tens of seconds per evaluation.
- Rejection sampling for prior draws scales exponentially with prior dimensionality.
- RFF approximation bias is more pronounced for Matern 5/2 kernels.
Experimental setup
Datasets: Hartmann (4D, 6D) Levy (5D) Rosenbrock (6D) Stybtang (7D) LCBench PD1 MF-Prior-Bench priors
Benchmarks: Hartmann (4D) Levy (5D) Hartmann (6D) Rosenbrock (6D) Stybtang (7D) LCBench PD1
Metrics: regret / best observed value vs iterations distance to acquisition argmax
Baselines: LogEI MES piBO decoupled Thompson sampling EI KG
Builds on: Decoupled posterior sampling (Wilson et al.) piBO BoTorch LogEI Max-value entropy search
Closest papers by meaning
- BONSAI: Bayesian Optimization with Natural Simplicity and Interpretability (NeurIPS 2026 · similarity 0.89)
- FunBO: Discovering Acquisition Functions for Bayesian Optimization with FunSearch (ICML 2025 · similarity 0.89)
- Cost-aware Bayesian Optimization via the Pandora's Box Gittins Index (NeurIPS 2024 · similarity 0.89)
- Batched Energy-Entropy acquisition for Bayesian Optimization (NeurIPS 2024 · similarity 0.88)
- Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimization (NeurIPS 2024 · similarity 0.88)
- Optimizing the Unknown: Black Box Bayesian Optimization with Energy-Based Model and Reinforcement Learning (NeurIPS 2025 · similarity 0.88)
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