Asymptotic Theory for IV-Based Reinforcement Learning with Potential Endogeneity

• URL: http://arxiv.org/abs/2103.04021v3
• Date: Tue, 24 Dec 2024 05:20:59 GMT
• Title: Asymptotic Theory for IV-Based Reinforcement Learning with Potential Endogeneity
• Authors: Jin Li, Ye Luo, Zigan Wang, Xiaowei Zhang,
• Abstract summary: We show that the dynamic interaction between data generation and data analysis leads to a new type of bias -- reinforcement bias.<n>We propose a class of instrument variable (IV)-based reinforcement learning (RL) algorithms to correct for the bias.<n>We provide formulas for inference on optimal policies of the IVRL algorithms.
• Score: 7.470941567346781
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 dependencies of the Markovian environment affect the inference.

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