  We present a novel $l_1$ regularized off-policy convergent TD-learning method
(termed RO-TD), which is able to learn sparse representations of value
functions with low computational complexity. The algorithmic framework
underlying RO-TD integrates two key ideas: off-policy convergent gradient TD
methods, such as TDC, and a convex-concave saddle-point formulation of
non-smooth convex optimization, which enables first-order solvers and feature
selection using online convex regularization. A detailed theoretical and
experimental analysis of RO-TD is presented. A variety of experiments are
presented to illustrate the off-policy convergence, sparse feature selection
capability and low computational cost of the RO-TD algorithm.
