# Transferring Information Across Interventions in Causal Bayesian Optimization

arXiv: https://arxiv.org/abs/2606.01457 · HTML: https://mlsanity.com/paper/2606.01457/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 31 May 2026.

## Builds on (most cited first, 23 of 23)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [YAHPO Gym -- An Efficient Multi-Objective Multi-Fidelity Benchmark for Hyperparameter Optimization](https://mlsanity.com/paper/2109.03670/) (2021)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Benchmarking the Performance of Bayesian Optimization across Multiple Experimental Materials Science Domains](https://mlsanity.com/paper/2106.01309/) (2021)
- [Neural Contextual Bandits without Regret](https://mlsanity.com/paper/2107.03144/) (2021)
- [Causal Bayesian Optimization](https://mlsanity.com/paper/2005.11741/) (2020)
- [Thinking inside the box: A tutorial on grey-box Bayesian optimization](https://mlsanity.com/paper/2201.00272/) (2022)
- [Cost-aware Bayesian Optimization via the Pandora's Box Gittins Index](https://mlsanity.com/paper/2406.20062/) (2024)
- [Regret Bounds for Expected Improvement Algorithms in Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2203.07875/) (2022)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Improved Regret Bounds for Gaussian Process Upper Confidence Bound in Bayesian Optimization](https://mlsanity.com/paper/2506.01393/) (2025)
- [Global Optimization of Gaussian Process Acquisition Functions Using a Piecewise-Linear Kernel Approximation](https://mlsanity.com/paper/2410.16893/) (2024)
- [Constrained Causal Bayesian Optimization](https://mlsanity.com/paper/2305.20011/) (2023)
- [Functional Causal Bayesian Optimization](https://mlsanity.com/paper/2306.06409/) (2023)
- [Adversarial Causal Bayesian Optimization](https://mlsanity.com/paper/2307.16625/) (2023)
- [Causal Bayesian Optimization via Exogenous Distribution Learning](https://mlsanity.com/paper/2402.02277/) (2024)
- [Multi-Objective Multi-Fidelity Bayesian Optimization with Causal Priors](https://mlsanity.com/paper/2602.00788/) (2026)
- [Extending Multi-Source Bayesian Optimization With Causality Principles](https://mlsanity.com/paper/2602.14791/) (2026)

## Abstract (arXiv)

Bayesian optimization is a popular way to optimize expensive systems, where every experiment, simulation, or intervention costs time or money. In its standard form, it treats the variables we control as plain inputs to a black box and cannot tell apart mere correlation from a real cause and effect. Causal Bayesian optimization closes part of this gap by using a known causal graph together with observational data to decide which variables are worth intervening on. Existing methods, however, learn the effect of each possible intervention almost in isolation, even though in a causal system these effects usually share the same underlying mechanisms. We propose graph-coupled causal Bayesian optimization, which ties the different intervention effects together through the uncertainty we have about a small set of shared causal parameters. The result is a causal kernel that lets evidence collected from one intervention improve our estimate of related interventions. For identifiable linear Gaussian causal models, we show that this kernel has low rank, bounded by the number of shared parameters rather than by the size of the intervention menu. This in turn yields an information-gain bound that grows only logarithmically in the optimization horizon, and a regret bound that cleanly separates three sources of error: optimization, causal estimation, and the choice of which intervention sets to consider. We also describe nonlinear and adaptive extensions. Across theory-aligned Gaussian systems, shared-mechanism stress tests, and standard causal optimization benchmarks, the method keeps the benefits of causal Bayesian optimization while transferring information across related interventions, with the clearest gains when direct interventions on the target's parents are unavailable and sparse interventional data must be reused across a large family of candidate interventions.