Bayesian Optimization using Partially Observable Gaussian Process Network

Bayesian Optimization (BO) is a highly successful technique for the optimization of noisy functions, but it can be difficult to scale. Gaussian Process Networks (GPN) replace a single black-box approximation with a network of connected noisy functions. This exploits sparsity in the causal links between process variables and improves the sample complexity for approximating the target function. In addition to the GPN setting, in many real-world process networks, we observe not only the final output but also intermediate observations. For example, by adding sensor instrumentation within a \enquote{black-box} process network. These intermediate observations are often incomplete and noisy. We propose Partially Observable Gaussian Process Network (POGPN), and its inference method, which addresses the limitations of GPN by handling noisy observations and uncertainty propagation while incorporating the structural knowledge of the process network. We empirically show superior performance of POGPN for Bayesian Optimization using benchmark functions and an ODE-based Penicillin production process.