Towards Estimating Bounds on the Effect of Policies under Unobserved Confounding

As many practical fields transition to provide personalized decisions, data is increasingly relevant to support the evaluation of candidate plans and policies (e.g., guidelines for the treatment of disease, government directives, etc.). In the machine learning literature, significant efforts have been put into developing machinery to predict the effectiveness of policies efficiently. The challenge is that, in practice, the effectiveness of a candidate policy is not always identifiable, i.e., not uniquely estimable from the combination of the available data and assumptions about the domain at hand (e.g., encoded in a causal graph). In this paper, we develop graphical characterizations and estimation tools to bound the effect of policies given a causal graph and observational data collected in non-identifiable settings. Specifically, our contributions are two-fold: (1) we derive analytical bounds for general probabilistic and conditional policies that are tighter than existing results, (2) we develop an estimation framework to estimate bounds from finite samples, applicable in higher-dimensional spaces and continuously-valued data. We further show that the resulting estimators have favourable statistical properties such as fast convergence and robustness to model misspecification.