Asymptotic Theory for IV-Based Reinforcement Learning with Potential Endogeneity

Abstract:In the standard data analysis framework, data is collected (once and for all), and then data analysis is carried out. However, with the advancement of digital technology, decision-makers constantly analyze past data and generate new data through their decisions. We model this as a Markov decision process and show that the dynamic interaction between data generation and data analysis leads to a new type of bias -- reinforcement bias -- that exacerbates the endogeneity problem in standard data analysis. We propose a class of instrument variable (IV)-based reinforcement learning (RL) algorithms to correct for the bias and establish their theoretical properties by incorporating them into a stochastic approximation (SA) framework. Our analysis accommodates iterate-dependent Markovian structures and, therefore, can be used to study RL algorithms with policy improvement. We also provide formulas for inference on optimal policies of the IV-RL algorithms. These formulas highlight how intertemporal dependency of the Markovian environment affects the inference.

Machine Learning (stat.ML); Machine Learning (cs.LG); Econometrics (econ.EM); Optimization and Control (math.OC)

arXiv:2103.04021 [stat.ML]

(or arXiv:2103.04021v4 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2103.04021 Focus to learn more arXiv-issued DOI via DataCite

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