A Unified Framework of Policy Learning for Contextual Bandit with Confounding Bias and Missing Observations

Abstract: We study the offline contextual bandit problem, where we aim to acquire an optimal policy using observational data. However, this data usually contains two deficiencies: (i) some variables that confound actions are not observed, and (ii) missing observations exist in the collected data. Unobserved confounders lead to a confounding bias and missing observations cause bias and inefficiency problems. To overcome these challenges and learn the optimal policy from the observed dataset, we present a new algorithm called Causal-Adjusted Pessimistic (CAP) policy learning, which forms the reward function as the solution of an integral equation system, builds a confidence set, and greedily takes action with pessimism. With mild assumptions on the data, we develop an upper bound to the suboptimality of CAP for the offline contextual bandit problem.