$\ell_1$-Based Adaptive Identification under Quantized Observations with Applications
This work addresses the gap in adaptive identification for quantized observations using ℓ1-optimization, providing a robust method with theoretical guarantees for practitioners in engineering and social sciences.
The paper develops a novel ℓ1-based adaptive identification algorithm for quantized observations, proving global convergence without persistent excitation and showing asymptotically vanishing average regret. Application to real-world judicial sentencing data demonstrates superior performance.
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.