Bayesian Optimization of Protocols

Automated laboratories must choose both an experimental protocol and its operating conditions. Bayesian optimization of function networks exploits composition within a fixed protocol but does not model transfer across a library of related protocols. Optimizing such a library from noisy terminal responses alone remains challenging. ProtocolUCB uses reusable operations as units of transfer by composing shared Bayesian operation models and applying an upper confidence bound over protocol-condition pairs. Under correct model specification and regularity conditions, its posterior-mean recommendations approach the set of global maximizers almost surely. In synthetic experiments, compositional modeling lowers final simple regret relative to fixed-hyperparameter GP-UCB on compositional objectives. Across 16 protocols, sharing reduces mean protocol-wise simple regret by 22% at $T=40$ relative to an independent compositional model. This formulation extends Bayesian optimization from tuning a protocol to learning across a library of related experiments, providing a framework for automated laboratories.