We consider the problem of optimising an expensive-to-evaluate grey-box objective function, within a finite budget, where known side-information exists in the form of the causal structure between the design variables. Standard black-box optimisation ignores the causal structure, often making it inefficient and expensive. The few existing methods that consider the causal structure are myopic and do not fully accommodate the observation-intervention trade-off that emerges when estimating causal effects. In this paper, we show that the observation-intervention trade-off can be formulated as a non-myopic optimal stopping problem which permits an efficient solution. We give theoretical results detailing the structure of the optimal stopping times and demonstrate the generality of our approach by showing that it can be integrated with existing causal Bayesian optimisation algorithms. Experimental results show that our formulation can enhance existing algorithms on real and synthetic benchmarks.

翻译：我们考虑在有限预算内优化一个评估代价高昂的灰盒目标函数的问题，其中已知的侧信息以设计变量之间的因果结构形式存在。标准的黑盒优化忽略了因果结构，往往导致效率低下且成本高昂。少数考虑因果结构的现有方法是短视的，未能充分适应在估计因果效应时出现的观测-干预权衡。在本文中，我们证明了观测-干预权衡可以表述为一个允许高效求解的非短视最优停止问题。我们给出了详细刻画最优停止时间结构的理论结果，并通过展示该方法可与现有因果贝叶斯优化算法集成，证明了其通用性。实验结果表明，我们的公式能够在真实与合成基准上增强现有算法的性能。