  In real-world scenarios, datasets collected from randomized experiments are
often constrained by size, due to limitations in time and budget. As a result,
leveraging large observational datasets becomes a more attractive option for
achieving high-quality policy learning. However, most existing offline
reinforcement learning (RL) methods depend on two key
assumptions--unconfoundedness and positivity--which frequently do not hold in
observational data contexts. Recognizing these challenges, we propose a novel
policy learning algorithm, PESsimistic CAusal Learning (PESCAL). We utilize the
mediator variable based on front-door criterion to remove the confounding bias;
additionally, we adopt the pessimistic principle to address the distributional
shift between the action distributions induced by candidate policies, and the
behavior policy that generates the observational data. Our key observation is
that, by incorporating auxiliary variables that mediate the effect of actions
on system dynamics, it is sufficient to learn a lower bound of the mediator
distribution function, instead of the Q-function, to partially mitigate the
issue of distributional shift. This insight significantly simplifies our
algorithm, by circumventing the challenging task of sequential uncertainty
quantification for the estimated Q-function. Moreover, we provide theoretical
guarantees for the algorithms we propose, and demonstrate their efficacy
through simulations, as well as real-world experiments utilizing offline
datasets from a leading ride-hailing platform.
