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We study the offline contextual bandit problem, where we aim to acquire anoptimal policy using observational data. However, this data usually containstwo deficiencies: (i) some variables that confound actions are not observed,and (ii) missing observations exist in the collected data. Unobservedconfounders lead to a confounding bias and missing observations cause bias andinefficiency problems. To overcome these challenges and learn the optimalpolicy from the observed dataset, we present a new algorithm calledCausal-Adjusted Pessimistic (CAP) policy learning, which forms the rewardfunction as the solution of an integral equation system, builds a confidenceset, and greedily takes action with pessimism. With mild assumptions on thedata, we develop an upper bound to the suboptimality of CAP for the offlinecontextual bandit problem.

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