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We study offline reinforcement learning under a novel model called strategicMDP, which characterizes the strategic interactions between a principal and asequence of myopic agents with private types. Due to the bilevel structure andprivate types, strategic MDP involves information asymmetry between theprincipal and the agents. We focus on the offline RL problem, where the goal isto learn the optimal policy of the principal concerning a target population ofagents based on a pre-collected dataset that consists of historicalinteractions. The unobserved private types confound such a dataset as theyaffect both the rewards and observations received by the principal. We proposea novel algorithm, Pessimistic policy Learning with Algorithmic iNstruments(PLAN), which leverages the ideas of instrumental variable regression and thepessimism principle to learn a near-optimal principal's policy in the contextof general function approximation. Our algorithm is based on the criticalobservation that the principal's actions serve as valid instrumental variables.In particular, under a partial coverage assumption on the offline dataset, weprove that PLAN outputs a $1 / \sqrt{K}$-optimal policy with $K$ being thenumber of collected trajectories. We further apply our framework to somespecial cases of strategic MDP, including strategic regression, strategicbandit, and noncompliance in recommendation systems.

Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instruments