Safe Bayesian Optimization for Uncertain Correlations Matrices in Linear Models of Co-Regionalization
It provides a safer and more flexible approach for multi-task Bayesian optimization, which is important for applications requiring reliable optimization under uncertainty.
The paper extends safety guarantees for multi-task Bayesian optimization to linear models of co-regionalization, deriving uniform error bounds and showing performance improvements on a benchmark.
This paper extends safety guarantees for multi-task Bayesian optimization with uncertain correlation matrices from intrinsic co-reginalization models to linear models of co-reginalization. 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-reginalization kernel. Furthermore, we show the potential improvement of performance using linear models of co-reginalization in a numerical comparison on a safe multi-task Bayesian optimization benchmark.