Self-fulfilling Bandits: Dynamic Selection in Algorithmic Decision-making

56 Pages Posted: 31 Aug 2021 Last revised: 19 Oct 2021

See all articles by Jin Li

Jin Li

Faculty of Business and Economics, The University of Hong Kong

Ye Luo

Faculty of Business and Economics, The University of Hong Kong

Xiaowei Zhang

Faculty of Business and Economics, The University of Hong Kong

Date Written: October 19, 2021

Abstract

This paper identifies and addresses dynamic selection problems that arise in online learning algorithms with endogenous data. In a contextual multi-armed bandit model, we show that a novel bias (self-fulfilling bias) arises because the endogeneity of the data influences the choices of decisions, affecting the distribution of future data to be collected and analyzed. We propose a class of algorithms to correct for the bias by incorporating instrumental variables into leading online learning algorithms. These algorithms lead to the true parameter values and meanwhile attain low (logarithmic-like) regret levels. We further prove a central limit theorem for statistical inference of the parameters of interest. To establish the theoretical properties, we develop a general technique that untangles the interdependence between data and actions.

Keywords: Self-fulfilling Bias, Dynamic Selection, Endogeneity Spillover, Contextual Multi-armed Bandit Model

Suggested Citation

Li, Jin and Luo, Ye and Zhang, Xiaowei, Self-fulfilling Bandits: Dynamic Selection in Algorithmic Decision-making (October 19, 2021). Available at SSRN: https://ssrn.com/abstract=3912989 or http://dx.doi.org/10.2139/ssrn.3912989

Jin Li

Faculty of Business and Economics, The University of Hong Kong ( email )

Pokfulam Road
Hong Kong, Pokfulam HK
Hong Kong

Ye Luo

Faculty of Business and Economics, The University of Hong Kong ( email )

Hong Kong

Xiaowei Zhang (Contact Author)

Faculty of Business and Economics, The University of Hong Kong ( email )

Pokfulam Road
Hong Kong
Hong Kong

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