Off-policy Evaluation for Multiple Actions in the Presence of Unobserved Confounders

Off-policy evaluation (OPE) is a crucial problem in reinforcement learning (RL), where the goal is to estimate the long-term cumulative reward of a target policy using historical data generated by a potentially different behaviour policy. In many real-world applications, such as precision medicine and recommendation systems, unobserved confounders may influence the action, reward, and state transition dynamics, which leads to biased estimates if not properly addressed. While existing methods for handling unobserved confounders in OPE focus on single-action settings, they are less effective in multi-action scenarios commonly found in practical applications, where an agent can take multiple actions simultaneously. In this paper, we propose a novel auxiliary variable-aided method for OPE in multi-action settings with unobserved confounders. Our approach overcomes the limitations of traditional auxiliary variable methods for multi-action scenarios by requiring only a single auxiliary variable, relaxing the need for as many auxiliary variables as the actions. Through theoretical analysis, we prove that our method provides an unbiased estimation of the target policy value. Empirical evaluations demonstrate that our estimator achieves better performance compared to existing baseline methods, highlighting its effectiveness and reliability in addressing unobserved confounders in multi-action OPE settings.