Safe Bayesian Optimization for Uncertain Correlation Matrices in Linear Models of Co-Regionalization

TL;DR

This paper enhances safety guarantees in multi-task Bayesian optimization by extending to linear models of co-regionalization, enabling more flexible correlation modeling and demonstrating improved performance in benchmarks.

Contribution

It introduces uniform error bounds for linear co-regionalization models and shows their advantages over intrinsic models in safe Bayesian optimization.

Findings

Derived uniform error bounds for linear co-regionalization kernels.

Showed performance gains in a safe multi-task Bayesian optimization benchmark.

Abstract

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.