Causal Intelligence for Constraint-Aware Intervention Design to Induce State Transitions

Causal Bayesian Optimization (CBO) combines causal inference with Bayesian optimization to enable sample-efficient intervention selection in systems with causal structure. This survey provides a systematic review of CBO through a unified BO-loop perspective, showing how causal assumptions shape intervention search spaces, surrogate models, acquisition functions, and decision policies. We organize existing methods by graph and system-knowledge assumptions, environment, intervention representation, surrogate architecture, and decision rule, and connect CBO to causal bandits, Bayesian experimental design, safe optimization, policy search, and causal abstraction. We also introduce a reproducibility-oriented benchmark spanning hard- and soft-intervention settings, with standardized GAP and a new trajectory-aware Path-Aware GAP (PA-GAP), evaluating seven CBO methods and a non-causal BO baseline across thirteen datasets, three budgets, and two metrics. Results show that no method dominates uniformly: rankings depend on dataset, budget, metric, and how causal information is used, while strong non-causal baselines remain competitive in several settings. Controlled graph-misspecification and omitted-variable stress tests further show that rankings can change substantially when learner-side causal information is perturbed. We conclude by identifying key open challenges, including robustness to causal-assumption violations, scalable unknown-graph optimization, mixed intervention types, realistic cost models, stronger theoretical guarantees, and integration with modern representation learning and causal abstractions.

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.

Uncovering the causal mechanisms of complex real-world systems remains a significant challenge, as these systems often entail high data collection costs and involve unknown interventions. We introduce MetaCaDI, the first framework to cast the identification of unknown interventions as a meta-learning problem, explicitly leveraging a jointly learned causal graph. MetaCaDI is a Bayesian framework that learns a shared causal structure across multiple environments and is optimized to rapidly adapt to new, few-shot intervention target identification tasks. A key innovation is our model's analytical adaptation, which uses a closed-form solution to bypass expensive and potentially unstable gradient-based bilevel optimization. Extensive experiments on synthetic and complex gene expression data demonstrate that MetaCaDI significantly outperforms state-of-the-art methods. It excels at identifying intervention targets from as few as 3 samples - where existing methods collapse to random chance - while robustly recovering the shared causal graph, proving its effectiveness in data-scarce scenarios.