  Learning the value function of a given policy (target policy) from the data
samples obtained from a different policy (behavior policy) is an important
problem in Reinforcement Learning (RL). This problem is studied under the
setting of off-policy prediction. Temporal Difference (TD) learning algorithms
are a popular class of algorithms for solving the prediction problem. TD
algorithms with linear function approximation are shown to be convergent when
the samples are generated from the target policy (known as on-policy
prediction). However, it has been well established in the literature that
off-policy TD algorithms under linear function approximation diverge. In this
work, we propose a convergent on-line off-policy TD algorithm under linear
function approximation. The main idea is to penalize the updates of the
algorithm in a way as to ensure convergence of the iterates. We provide a
convergence analysis of our algorithm. Through numerical evaluations, we
further demonstrate the effectiveness of our algorithm.
