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

• URL: http://arxiv.org/abs/2303.11187v1
• Date: Mon, 20 Mar 2023 15:17:31 GMT
• Title: A Unified Framework of Policy Learning for Contextual Bandit with Confounding Bias and Missing Observations
• Authors: Siyu Chen, Yitan Wang, Zhaoran Wang, Zhuoran Yang
• Abstract summary: We study the offline contextual bandit problem, where we aim to acquire an optimal policy using observational data. 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.
• Score: 108.89353070722497
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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