$\ell_1$-Based Adaptive Identification under Quantized Observations with Applications

TL;DR

This paper introduces a new $$-based adaptive identification algorithm tailored for quantized data, demonstrating theoretical convergence and practical effectiveness through real-world judicial sentencing applications.

Contribution

The paper presents a novel $$-based adaptive identification method for quantized observations, with proven global convergence without persistent excitation, and showcases its application to real-world data.

Findings

Global convergence of the proposed algorithm is established.

Average regret diminishes as data size increases.

Application to judicial sentencing data shows superior performance.

Abstract

Quantized observations are ubiquitous in a wide range of applications across engineering and the social sciences, and algorithms based on the $\ell_1$-norm are well recognized for their robustness to outliers compared with their $\ell_2$-based counterparts. Nevertheless, adaptive identification methods that integrate quantized observations with $\ell_1$-optimization remain largely underexplored. Motivated by this gap, we develop a novel $\ell_1$-based adaptive identification algorithm specifically designed for quantized observations. Without relying on the traditional persistent excitation condition, we establish global convergence of the parameter estimates to their true values and show that the average regret asymptotically vanishes as the data size increases. Finally, we apply our new identification algorithm to a judicial sentencing problem using real-world data, which demonstrates its superior performance and practical significance.