Recursive $\ell_{1,\infty}$ Group lasso

TL;DR

This paper presents a recursive adaptive group lasso algorithm for real-time sparse prediction, efficiently updating predictor coefficients with lower computational complexity and improved performance over existing methods.

Contribution

It introduces an online homotopy method for exact updates of $\, ext{l}_{1, ext{infinity}}$-penalized RLS, enabling real-time group sparse system identification.

Findings

Outperforms $\, ext{l}_1$ regularized RLS in simulations

Reduces computational complexity compared to direct group lasso solvers

Provides exact updates for $\, ext{l}_{1, ext{infinity}}$-penalized RLS

Abstract

We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an exact update of the optimal $\ell_{1,\infty}$-penalized recursive least squares (RLS) predictor. Each update minimizes a convex but nondifferentiable function optimization problem. We develop an online homotopy method to reduce the computational complexity. Numerical simulations demonstrate that the proposed algorithm outperforms the $\ell_1$ regularized RLS algorithm for a group sparse system identification problem and has lower implementation complexity than direct group lasso solvers.