We propose functional causal Bayesian optimization (fCBO), a method for finding interventions that optimize a target variable in a known causal graph. fCBO extends the CBO family of methods to enable functional interventions, which set a variable to be a deterministic function of other variables in the graph. fCBO models the unknown objectives with Gaussian processes whose inputs are defined in a reproducing kernel Hilbert space, thus allowing to compute distances among vector-valued functions. In turn, this enables to sequentially select functions to explore by maximizing an expected improvement acquisition functional while keeping the typical computational tractability of standard BO settings. We introduce graphical criteria that establish when considering functional interventions allows attaining better target effects, and conditions under which selected interventions are also optimal for conditional target effects. We demonstrate the benefits of the method in a synthetic and in a real-world causal graph.

翻译：我们提出功能因果贝叶斯优化（fCBO），一种在已知因果图中寻找优化目标变量的干预方法。fCBO扩展了CBO方法族以支持功能干预，即将变量设为图中其他变量的确定性函数。fCBO通过高斯过程对未知目标建模，其输入定义在再生核希尔伯特空间中，从而能够计算向量值函数间的距离。进而，该方法通过最大化期望改进获取泛函，顺序选择待探索函数，同时保持标准贝叶斯优化设置的计算可行性。我们引入图论判据，建立何时考虑功能干预能获得更好的目标效应，以及所选干预在何种条件下对条件目标效应同样最优。我们通过合成因果图与真实世界因果图验证了该方法的有效性。