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.

本文提出了一种基于模型和因果贝叶斯优化算法的方法，学习一个完整的系统模型并通过乐观的原则进行探索和开发，以解决在未知结构方程模型下如何干预以最大化目标变量的问题，并通过实验得到了有益的结果。