The famous Policy Iteration algorithm alternates between policy improvement
and policy evaluation. Implementations of this algorithm with several variants
of the latter evaluation stage, e.g, n-step and trace-based returns, have
been analyzed in previous works. However, the case of multiple-step lookahead
policy improvement, despite the recent increase in empirical evidence of its
strength, has to our knowledge not been carefully analyzed yet. In this work,
we introduce the first such analysis. Namely, we formulate variants of
multiple-step policy improvement, derive new algorithms using these definitions
and prove their convergence. Moreover, we show that recent prominent
Reinforcement Learning algorithms are, in fact, instances of our framework. We
thus shed light on their empirical success and give a recipe for deriving new
algorithms for future study.Comment: ICML 201
