Recursive $\ell _{1,\infty }$ Group Lasso

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 ℓ_1,∞-penalized recursive least squares (RLS) predictor. Each update minimizes a convex but nondifferentiable function optimization problem. We develop an on-line homotopy method to reduce the computational complexity. Numerical simulations demonstrate that the proposed algorithm outperforms the ℓ₁ regularized RLS algorithm for a group sparse system identification problem and has lower implementation complexity than direct group lasso solvers.