Bidirectional Information Flow (BIF) -- A Sample Efficient Hierarchical Gaussian Process for Bayesian Optimization

Hierarchical Gaussian Process (H-GP) models divide problems into different subtasks, allowing for different models to address each part, making them well-suited for problems with inherent hierarchical structure. However, typical H-GP models do not fully take advantage of this structure, only sending information up or down the hierarchy. This one-way coupling limits sample efficiency and slows convergence. We propose Bidirectional Information Flow (BIF), an efficient H-GP framework that establishes bidirectional information exchange between parent and child models in H-GPs for online training. BIF retains the modular structure of hierarchical models - the parent combines subtask knowledge from children GPs - while introducing top-down feedback to continually refine children models during online learning. This mutual exchange improves sample efficiency, enables robust training, and allows modular reuse of learned subtask models. BIF outperforms conventional H-GP Bayesian Optimization methods, achieving up to 85% and 5x higher $R^2$ scores for the parent and children respectively, on synthetic and real-world neurostimulation optimization tasks.

@article{guerra2025_2505.11294,
  title={ Bidirectional Information Flow (BIF) -- A Sample Efficient Hierarchical Gaussian Process for Bayesian Optimization },
  author={ Juan D. Guerra and Thomas Garbay and Guillaume Lajoie and Marco Bonizzato },
  journal={arXiv preprint arXiv:2505.11294},
  year={ 2025 }
}