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

arXiv: https://arxiv.org/abs/2505.11294 · HTML: https://mlsanity.com/paper/2505.11294/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 6 of 6)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Transfer Learning with Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2111.11223/) (2021)
- [BILBO: BILevel Bayesian Optimization](https://mlsanity.com/paper/2502.02121/) (2025)

## Abstract (arXiv)

Hierarchical Gaussian Process (H-GP) models divide problems into different subtasks, allowing different components to address each part, making them well-suited for problems with inherent compositional structure. However, existing H-GP frameworks typically employ one-way information sharing - either top-down or bottom-up - which limits sample efficiency and slows convergence. We propose Bidirectional Information Flow (BIF), which establishes continuous two-way communication. BIF retains the modular structure of hierarchical models-the parent conditions its own posterior on child summaries, treating them as structured priors-while introducing top-down feedback to softly decompose environment observations from the parent into sub-responses. This mutual exchange improves sample efficiency, enables robust training, and allows modular reuse of learned subtask models. We prove analytically that the regret of a GP with a learned kernel scales linearly with the mismatch to the true kernel, tightening in the hierarchical case to the sum of child-level errors. Ablation shows that removing the downward pathway collapses child R2 by up to 58%. Across synthetic, neurostimulation, and HPO benchmarks, BIF achieves up to 4× higher parent R2 and ~ 100% AUC improvement over vanilla GPBO, and outscores all hierarchical state-of-the-art methods on child R2 given the correct acquisition function, while supporting modular child transfer to novel composite tasks.