  Feature selection and regularization are becoming increasingly prominent
tools in the efforts of the reinforcement learning (RL) community to expand the
reach and applicability of RL. One approach to the problem of feature selection
is to impose a sparsity-inducing form of regularization on the learning method.
Recent work on $L_1$ regularization has adapted techniques from the supervised
learning literature for use with RL. Another approach that has received renewed
attention in the supervised learning community is that of using a simple
algorithm that greedily adds new features. Such algorithms have many of the
good properties of the $L_1$ regularization methods, while also being extremely
efficient and, in some cases, allowing theoretical guarantees on recovery of
the true form of a sparse target function from sampled data. This paper
considers variants of orthogonal matching pursuit (OMP) applied to
reinforcement learning. The resulting algorithms are analyzed and compared
experimentally with existing $L_1$ regularized approaches. We demonstrate that
perhaps the most natural scenario in which one might hope to achieve sparse
recovery fails; however, one variant, OMP-BRM, provides promising theoretical
guarantees under certain assumptions on the feature dictionary. Another
variant, OMP-TD, empirically outperforms prior methods both in approximation
accuracy and efficiency on several benchmark problems.
