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

2026-05-13

AI Summary

This work addresses safety assurance in multi-task Bayesian optimization under uncertain inter-task correlation structures by extending the safe Bayesian optimization framework from intrinsic coregionalization models to the more expressive linear model of coregionalization (LMC) Gaussian processes. By flexibly modeling task correlations through a combination of multiple basis features, the proposed approach enhances representational capacity while maintaining safety guarantees. The key theoretical contribution lies in establishing uniform error bounds for vector-valued Gaussian processes, which serve as the foundation for providing rigorous and unified safety assurances across all tasks. Empirical evaluations on standard safe multi-task optimization benchmarks demonstrate that the method consistently outperforms conventional approaches, effectively balancing optimization performance with strict adherence to safety constraints.

Abstract

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.

Problem

• Bayesian Optimization
• Safety
• Linear Model of Co-regionalization
• Uncertain Correlation Matrices
• Multi-task

Innovation

• safe Bayesian optimization
• linear model of co-regionalization
• multi-task learning
• Gaussian process
• uncertain correlation matrices