Bayesian Optimization on Networks
This work addresses optimization challenges in domains like telecommunications where functions are costly to evaluate, though it is incremental as it adapts existing Bayesian optimization methods to network-specific geometries.
The paper tackles the problem of optimizing expensive black-box functions on networks modeled as metric graphs by developing Bayesian optimization algorithms with Gaussian process surrogates tailored to the network geometry, achieving effectiveness in benchmark tests and Bayesian inversion applications.
This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that sequentially update a Gaussian process surrogate model of the objective to guide the acquisition of query points. To ensure that the surrogates are tailored to the network's geometry, we adopt Whittle-Matérn Gaussian process prior models defined via stochastic partial differential equations on metric graphs. In addition to establishing regret bounds for optimizing sufficiently smooth objective functions, we analyze the practical case in which the smoothness of the objective is unknown and the Whittle-Matérn prior is represented using finite elements. Numerical results demonstrate the effectiveness of our algorithms for optimizing benchmark objective functions on a synthetic metric graph and for Bayesian inversion via maximum a posteriori estimation on a telecommunication network.