Model-based Causal Bayesian Optimization
This addresses a key challenge in causal inference for applications like medicine and manufacturing, offering a novel approach with theoretical guarantees, though it builds incrementally on existing CBO work.
The paper tackles the problem of optimizing interventions in unknown structural equation models, known as causal Bayesian optimization (CBO), by proposing the MCBO algorithm that learns a full system model and provides non-asymptotic regret bounds, showing favorable empirical performance compared to state-of-the-art methods.
How should we intervene on an unknown structural equation model to maximize a downstream variable of interest? This setting, also known as causal Bayesian optimization (CBO), has important applications in medicine, ecology, and manufacturing. Standard Bayesian optimization algorithms fail to effectively leverage the underlying causal structure. Existing CBO approaches assume noiseless measurements and do not come with guarantees. We propose the model-based causal Bayesian optimization algorithm (MCBO) that learns a full system model instead of only modeling intervention-reward pairs. MCBO propagates epistemic uncertainty about the causal mechanisms through the graph and trades off exploration and exploitation via the optimism principle. We bound its cumulative regret, and obtain the first non-asymptotic bounds for CBO. Unlike in standard Bayesian optimization, our acquisition function cannot be evaluated in closed form, so we show how the reparameterization trick can be used to apply gradient-based optimizers. The resulting practical implementation of MCBO compares favorably with state-of-the-art approaches empirically.