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Principled Bayesian Optimization in Collaboration with Human Experts
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Proposes COBOL, a Bayesian optimisation method that uses binary accept/reject labels from human experts with a likelihood-ratio confidence set for the expert belief, a primal-dual acquisition, and data-driven trust adjustment, with handover and no-harm guarantees.
Problem
Bayesian optimisation with human experts who give noisy, possibly adversarial binary accept/reject labels on query points, where expert labels are costly and the optimiser must decide how much to trust them.
Approach
Model the expert as a binary labeller with a latent belief function g in an RKHS, estimate a likelihood-ratio confidence set for g, and mix expert-augmented LCB candidates with vanilla LCB via a primal-dual weight, with a data-driven doubling rule for the norm bound B_g so the expert's influence is adjusted automatically (no-harm guarantee) while expert queries become sublinear (handover guarantee
Key results
- On the real-world battery tasks, the method outperformed all baselines in the first two tasks, and in the new-materials tasks where expert advice was unreliable it matched the distrustful algorithm and vanilla LCB rather than failing.
- Robustness experiments on Ackley show accelerated convergence for informative labels (a=1,2) and convergence on par with vanilla LCB for random or adversarial labels (a=0,-1,-2).
- Theory gives cumulative regret O(gamma_T sqrt(T)) independent of g and expert query count sublinear in T (e.g., O((log T)^3) for linear kernel).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add expert advice with data-driven trust adjustment | COBOL · 4D Ackley, informative expert labels (a = 1, 2) | simple regret | Helped |
| add expert advice with data-driven trust adjustment | COBOL · 4D Ackley, random or adversarial expert labels (a = 0, -1, -2) | cumulative regret | No clear effect |
| use expert advice with data-driven trust adjustment | COBOL · standard electrolyte composition and solvent-modified electrolyte | convergence | Helped |
| use data-driven trust adjustment instead of fixed strong trust | COBOL · polymer-nanocomposite electrolyte and ionic liquid | convergence | Helped |
| sample directly from the expert belief instead of random sampling | Expert sampling · synthetic functions | convergence | Helped |
| use expert sampling instead of vanilla LCB | Expert sampling · synthetic functions | convergence | Mixed |
| use the primal-dual mixing objective (λ₀ = 1 or 2) instead of λ₀ = 0 (ablation) | COBOL · 4D Ackley | convergence | Helped |
| vary η, λ₀, and g_thr (ablation) | COBOL · 4D Ackley | convergence | No clear effect |
| use a windowed model that forgets old expert labels (ablation) | COBOL · Bayesian optimization with time-varying human knowledge | performance | No clear effect |
| use binary labels rather than alternative feedback forms (ablation) | COBOL · expert-feedback experiments | performance | Helped |
| reduce expert-label requests as the model becomes confident | COBOL · continuous-domain Bayesian optimization | expert queries | Helped |
Surprising findings
- Expert sampling for the new-materials tasks was worse than random sampling, so the method learned to distrust experts there.
Limitations
- Based on GP-UCB, so it shares its limitations such as poor scaling to high dimensions.
- Assumes stationary expert knowledge and a single expert; multi-expert and batch settings are left to future work.
- Theoretical acceleration guarantees are not provided; robustness is prioritised over acceleration.
Experimental setup
Datasets: Ackley function Rosenbrock function lithium-ion battery electrolyte design data
Benchmarks: Ackley Rosenbrock battery electrolyte design tasks with human experts
Metrics: cumulative regret simple regret cumulative expert queries
Baselines: vanilla LCB random sampling expert sampling constrained BO baselines
Builds on: GP-UCB constrained Bayesian optimization
Closest papers by meaning
- Bayesian Optimization from Human Feedback: Near-Optimal Regret Bounds (ICML 2025 · similarity 0.87)
- Bayesian Decision Making around Experts (NeurIPS 2026 · similarity 0.86)
- Regional Expected Improvement for Efficient Trust Region Selection in High-Dimensional Bayesian Optimization (AAAI 2025 · similarity 0.86)
- Exploiting Human-AI Dependence for Learning to Defer (ICML 2024 · similarity 0.86)
- Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents (ICML 2025 · similarity 0.85)
- Bayesian Inference for Correlated Human Experts and Classifiers (ICML 2025 · similarity 0.85)
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