Model-based Causal Bayesian Optimization

TL;DR

This paper introduces MCBO, a model-based causal Bayesian optimization algorithm that learns causal models to optimize interventions effectively, providing theoretical guarantees and practical advantages over existing methods.

Contribution

The paper presents MCBO, the first approach to provide non-asymptotic regret bounds for causal Bayesian optimization by learning full causal models and using gradient-based optimization.

Findings

MCBO outperforms state-of-the-art methods empirically.

Provides the first non-asymptotic regret bounds for CBO.

Uses reparameterization trick for gradient-based optimization.

Abstract

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.