We explore algorithms to select actions in the causal bandit setting where the learner can choose to intervene on a set of random variables related by a causal graph, and the learner sequentially chooses interventions and observes a sample from the interventional distribution. The learner's goal is to quickly find the intervention, among all interventions on observable variables, that maximizes the expectation of an outcome variable. We depart from previous literature by assuming no knowledge of the causal graph except that latent confounders between the outcome and its ancestors are not present. We first show that the unknown graph problem can be exponentially hard in the parents of the outcome. To remedy this, we adopt an additional additive assumption on the outcome which allows us to solve the problem by casting it as an additive combinatorial linear bandit problem with full-bandit feedback. We propose a novel action-elimination algorithm for this setting, show how to apply this algorithm to the causal bandit problem, provide sample complexity bounds, and empirically validate our findings on a suite of randomly generated causal models, effectively showing that one does not need to explicitly learn the parents of the outcome to identify the best intervention.

翻译：我们探索在因果赌博机设置中选择行动的算法，其中学习者可以选择干预一组由因果图关联的随机变量，并依次选择干预措施，观察来自干预分布的样本。学习者的目标是在所有可观测变量的干预中，快速找到能使结果变量期望最大化的干预。我们与先前文献的不同之处在于，假设除了结果变量与其祖先之间不存在潜在混杂因素外，对因果图一无所知。我们首先证明，未知图问题在结果变量的父节点数量上可能呈指数级困难。为解决此问题，我们对结果变量采用额外的加性假设，从而通过将其转化为具有全赌博机反馈的加性组合线性赌博机问题来求解。我们提出了一种新颖的行动消除算法，展示了如何将该算法应用于因果赌博机问题，给出了样本复杂度界限，并在随机生成的因果模型套件上实证验证了我们的发现，有效地表明无需显式学习结果变量的父节点即可识别出最优干预措施。