  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.
