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We consider the problem of using expert data with unobserved confounders forimitation and reinforcement learning. We begin by defining the problem oflearning from confounded expert data in a contextual MDP setup. We analyze thelimitations of learning from such data with and without external reward, andpropose an adjustment of standard imitation learning algorithms to fit thissetup. We then discuss the problem of distribution shift between the expertdata and the online environment when the data is only partially observable. Weprove possibility and impossibility results for imitation learning underarbitrary distribution shift of the missing covariates. When additionalexternal reward is provided, we propose a sampling procedure that addresses theunknown shift and prove convergence to an optimal solution. Finally, wevalidate our claims empirically on challenging assistive healthcare andrecommender system simulation tasks.

On Covariate Shift of Latent Confounders in Imitation and Reinforcement Learning