Structural Estimation of Markov Decision Processes in High-Dimensional State Space with Finite-Time Guarantees

We consider the task of estimating a structural model of dynamic decisions by a human agent based on the observable history of implemented actions and visited states. This problem has an inherent nested structure: In the inner problem, an optimal policy for a given reward function is identified, whereas in the outer problem, a measure of fit is maximized. Several approaches have been proposed to alleviate the computational burden of this nested-loop structure, but these methods still suffer from high complexity when the state space is either discrete with large cardinality or continuous in high dimensions. Other approaches in the inverse reinforcement learning literature emphasize policy estimation at the expense of reduced reward estimation accuracy. In this paper, we propose a single-loop estimation algorithm with finite time guarantees that is equipped to deal with high-dimensional state spaces without compromising reward estimation accuracy. In the proposed algorithm, each policy improvement step is followed by a stochastic gradient step for likelihood maximization. We show the proposed algorithm converges to a stationary solution with a finite-time guarantee. Further, if the reward is parameterized linearly, the algorithm approximates the maximum likelihood estimator sublinearly.

Funding: M. Hong and S. Zeng are supported by the National Science Foundation [Grants EPCN-2311007 and CCF-1910385]. This work is also part of AI-CLIMATE: “AI Institute for Climate-Land Interactions, Mitigation, Adaptation, Tradeoffs and Economy” and is supported by the U.S. Department of Agriculture National Institute of Food and Agriculture and the National Science Foundation National AI Research Institutes [Competitive Award 2023-67021-39829]. A. Garcia is partially supported by the Army Research Office [Grant W911NF-22-1-0213].

Supplemental Material: The computer code and data that support the findings of this study are available within this article’s supplemental material at https://doi.org/10.1287/opre.2022.0511.