Dynamic Selection in Algorithmic Decision-making

TL;DR

This paper addresses the challenge of bias in online decision algorithms caused by endogenous data, proposing an instrumental-variable method to correct bias and achieve low regret with valid statistical inference.

Contribution

It introduces a novel instrumental-variable-based algorithm for dynamic selection in online learning, correcting bias and providing theoretical guarantees.

Findings

The algorithm achieves logarithmic regret levels.

A central limit theorem for inference is established.

A new technique untangles data-action interdependence.

Abstract

This paper identifies and addresses dynamic selection problems in online learning algorithms with endogenous data. In a contextual multi-armed bandit model, 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 an instrumental-variable-based algorithm to correct for the bias. It obtains true parameter values and attains low (logarithmic-like) regret levels. We also prove a central limit theorem for statistical inference. To establish the theoretical properties, we develop a general technique that untangles the interdependence between data and actions.