Heterogeneous ensembles built from the predictions of a wide variety and large number of diverse base predictors represent a potent approach to building predictive models for problems where the ideal base/individual predictor may not be obvious. Ensemble selection is an especially promising approach here, not only for improving prediction performance, but also because of its ability to select a collectively predictive subset, often a relatively small one, of the base predictors. In this paper, we present a set of algorithms that explicitly incorporate ensemble diversity, a known factor influencing predictive performance of ensembles, into a reinforcement learning framework for ensemble selection. We rigorously tested these approaches on several challenging problems and associated data sets, yielding that several of them produced more accurate ensembles than those that don't explicitly consider diversity. More importantly, these diversity-incorporating ensembles were much smaller in size, i.e., more parsimonious, than the latter types of ensembles. This can eventually aid the interpretation or reverse engineering of predictive models assimilated into the resultant ensemble(s).