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Efficient Inference for Inverse Reinforcement Learning and Dynamic Discrete Choice Models

In many sequential decision-making problems, researchers observe actions but not the rewards that drive behavior, yet still wish to evaluate and compare counterfactual policies. Inverse reinforcement learning (IRL) and dynamic discrete choice (DDC) models address this setting by positing an optimality model that links latent rewards to observed actions. Existing flexible IRL methods allow rich reward representations but typically do not provide valid inference, whereas classical DDC methods support inference only under restrictive parametric structure. We develop a semiparametric framework for debiased inverse reinforcement learning in maximum-entropy IRL and Gumbel-shock DDC models. Our key identification result is that the log-behavior policy can be treated as a pseudo-reward: it point-identifies policy value differences and, under a normalization constraint, the reward itself. This reduces inference on reward-dependent estimands to inference on smooth functionals of the behavior policy and transition kernel. We establish pathwise differentiability, derive efficient influence functions, and construct automatic debiased machine-learning estimators that permit flexible nuisance estimation while attaining $\sqrt{n}$-consistency, asymptotic normality, and semiparametric efficiency. The result is a computationally tractable framework for valid uncertainty quantification in flexible IRL and DDC models.

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