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.

翻译：我们应如何对未知结构方程模型进行干预，以最大化感兴趣的下游变量？这一设定，也称为因果贝叶斯优化（CBO），在医学、生态学和制造业中具有重要应用。标准贝叶斯优化算法无法有效利用潜在因果结构。现有CBO方法假设无噪声测量且不提供保证。我们提出基于模型的因果贝叶斯优化算法（MCBO），该算法学习完整系统模型，而非仅对干预-奖励对进行建模。MCBO通过图结构传播关于因果机制的认知不确定性，并基于乐观原则权衡探索与利用。我们给出了其累积遗憾的上界，获得了CBO的首个非渐近界。与标准贝叶斯优化不同，我们的采集函数无法以闭式求解，因此我们展示了如何利用重参数化技巧应用基于梯度的优化器。MCBO的实际实现方案在经验上优于现有最先进方法。