Efficient Federated Bayesian Optimization with Symbolic Regression Model

Federated Bayesian Optimization (FBO) enables collaborative optimization across distributed data sources without direct data exchange, addressing privacy concerns in domains such as healthcare and manufacturing. However, existing FBO approaches often suffer from high communication overhead and computational costs due to the complexity of sharing and updating Gaussian Process (GP) models across federated clients. This paper presents a novel framework that combines symbolic regression (SR) with GPs to create lightweight surrogate models for federated black-box optimization. Our approach employs SR to generate compact mathematical expressions for client-server communication while utilizing local GPs to model uncertainty, significantly reducing bandwidth requirements and computational complexity. The framework incorporates a Lower Confidence Bound sampling strategy that combines SR predictions with GP posterior distributions to balance exploration and exploitation. Experimental results demonstrate the reliability and efficacy of our proposed method on benchmark problems.