Minimax-Optimal Policy Learning Under Unobserved Confounding

We study the problem of learning personalized decision policies from observational data while accounting for possible unobserved confounding. Previous approaches, which assume unconfoundedness, that is, that no unobserved confounders affect both the treatment assignment as well as outcome, can lead to policies that introduce harm rather than benefit when some unobserved confounding is present as is generally the case with observational data. Instead, because policy value and regret may not be point-identifiable, we study a method that minimizes the worst-case estimated regret of a candidate policy against a baseline policy over an uncertainty set for propensity weights that controls the extent of unobserved confounding. We prove generalization guarantees that ensure our policy is safe when applied in practice and in fact obtains the best possible uniform control on the range of all possible population regrets that agree with the possible extent of confounding. We develop efficient algorithmic solutions to compute this minimax-optimal policy. Finally, we assess and compare our methods on synthetic and semisynthetic data. In particular, we consider a case study on personalizing hormone replacement therapy based on observational data, in which we validate our results on a randomized experiment. We demonstrate that hidden confounding can hinder existing policy-learning approaches and lead to unwarranted harm although our robust approach guarantees safety and focuses on well-evidenced improvement, a necessity for making personalized treatment policies learned from observational data reliable in practice.