Pearl's do calculus is a complete axiomatic approach to learn the identifiable causal effects from observational data. When such an effect is not identifiable, it is necessary to perform a collection of often costly interventions in the system to learn the causal effect. In this work, we consider the problem of designing the collection of interventions with the minimum cost to identify the desired effect. First, we prove that this problem is NP-hard, and subsequently propose an algorithm that can either find the optimal solution or a logarithmic-factor approximation of it. This is done by establishing a connection between our problem and the minimum hitting set problem. Additionally, we propose several polynomial-time heuristic algorithms to tackle the computational complexity of the problem. Although these algorithms could potentially stumble on sub-optimal solutions, our simulations show that they achieve small regrets on random graphs.

翻译：Pearl的do演算是一种完备的公理化方法，用于从观测数据中学习可识别的因果效应。当这种效应不可识别时，通常需要对系统执行一系列往往成本高昂的干预措施来学习该因果效应。本文考虑设计成本最小化的干预措施集合来识别所需效应的问题。首先，我们证明该问题属于NP难问题，随后提出一种能够找到最优解或对数因子近似解的算法。这是通过建立该问题与最小击中集问题之间的联系实现的。此外，我们提出若干多项式时间启发式算法来应对该问题的计算复杂性。尽管这些算法可能偶然得到次优解，但仿真结果表明它们在随机图上实现了较小的遗憾值。