PAG-CBO: Causal Bayesian Optimization under Partial Identification

Causal Bayesian optimization uses causal structure and observational data to reduce costly experimentation. With hidden confounding and uncertain structure, however, intervention effects may remain only partially identified. We introduce PAG-CBO for systems whose structural uncertainty is represented by a partial ancestral graph (PAG). Our method combines structural pruning with bounds on intervention-response means, accounts for observational sampling uncertainty, and updates these bounds using interventional data. It eliminates actions that cannot be near-optimal and stops when the remaining uncertainty permits an $ϵ$-optimality certificate. Under a correct PAG and simultaneous confidence-band coverage, we prove certificate validity and localize a standard kernel-bandit simple-regret bound to the region surviving observational pruning. In discrete benchmarks, informative positive-width causal bounds can certify a recommendation before any intervention; when these bounds do not settle the decision, sequential experiments reduce the remaining uncertainty. An empirical calibration study records no false recommendations among 4,835 stopping claims under correctly specified PAGs. When informative causal bounds are unavailable, PAG-CBO uses the known outcome range and relies on experimental learning.