Weighted importance sampling for off-policy learning with linear function approximation

Importance sampling is an essential component of off-policy model-free reinforcement learning algorithms. However, its most effective variant, \emph{weighted} importance sampling, does not carry over easily to function approximation and, because of this, it is not utilized in existing off-policy learning algorithms. In this paper, we take two steps toward bridging this gap. First, we show that weighted importance sampling can be viewed as a special case of weighting the error of individual training samples, and that this weighting has theoretical and empirical benefits similar to those of weighted importance sampling. Second, we show that these benefits extend to a new weighted-importance-sampling version of off-policy LSTD(lambda). We show empirically that our new WIS-LSTD(lambda) algorithm can result in much more rapid and reliable convergence than conventional off-policy LSTD(lambda) (Yu 2010, Bertsekas & Yu 2009).