Constrained Causal Bayesian Optimization
This work addresses the problem of constrained optimization in causal inference for researchers and practitioners, but it is incremental as it builds on existing Bayesian optimization methods by incorporating causal constraints.
The authors tackled the problem of optimizing interventions in a known causal graph under constraints by proposing constrained causal Bayesian optimization (cCBO), which reduces the search space using graph structure and observational data, then uses Gaussian processes and a constrained acquisition function to select interventions, showing successful trade-offs in convergence and feasibility on artificial and real-world graphs.
We propose constrained causal Bayesian optimization (cCBO), an approach for finding interventions in a known causal graph that optimize a target variable under some constraints. cCBO first reduces the search space by exploiting the graph structure and, if available, an observational dataset; and then solves the restricted optimization problem by modelling target and constraint quantities using Gaussian processes and by sequentially selecting interventions via a constrained expected improvement acquisition function. We propose different surrogate models that enable to integrate observational and interventional data while capturing correlation among effects with increasing levels of sophistication. We evaluate cCBO on artificial and real-world causal graphs showing successful trade off between fast convergence and percentage of feasible interventions.