Reinforcement Learning Based Computationally Efficient Conditional Choice Simulation Estimation of Dynamic Discrete Choice Models

Abstract

Dynamic discrete choice (DDC) models have found widespread application in marketing. However, estimating these becomes challenging in "big data" settings with high-dimensional state-action spaces. To address this challenge, this paper develops a Reinforcement Learning (RL)-based two-step ("computationally light") Conditional Choice Simulation (CCS) estimation approach that combines the scalability of machine learning with the transparency, explainability, and interpretability of structural models, which is particularly valuable for counterfactual policy analysis. The method is premised on three insights: (1) the CCS ("forward simulation") approach is a special case of RL algorithms, (2) starting from an initial state-action pair, CCS updates the corresponding value function only after each simulation path has terminated, whereas RL algorithms may update for all the state-action pairs visited along a simulated path, and (3) RL focuses on inferring an agent's optimal policy with known reward functions, whereas DDC models focus on estimating the reward functions presupposing optimal policies. The procedure's computational efficiency over CCS estimation is demonstrated using Monte Carlo simulations with a canonical machine replacement and a consumer food purchase model. Framing CCS estimation of DDC models as an RL problem increases their applicability and scalability to high-dimensional marketing problems while retaining both interpretability and tractability.