Safe Bayesian Optimization for Uncertain Correlation Matrices in Linear Models of Co-Regionalization
Authors: Jannis Lübsen, Annika Eichler
Organizations: Institute of Control Systems, Hamburg University of Technology, Hamburg, Germany · Institute of Control Systems, Hamburg University of Technology · Deutsches Elektronen-Synchrotron, Hamburg, Germany
This paper extends safety guarantees for multi-task Bayesian optimization with uncertain co-regionalization matrices from intrinsic co-regionalization models to linear models of co-regionalization. The latter allows for more flexible modeling of the inter-task correlations by composing multiple features. We derive uniform error bounds for vector-valued functions sampled from a Gaussian process with a linear model of co-regionalization kernel. Furthermore, we show the potential performance gains of linear models of co-regionalization in a numerical comparison on a safe multi-task Bayesian optimization benchmark.