  We apply functional acceleration to the Policy Mirror Descent (PMD) general
family of algorithms, which cover a wide range of novel and fundamental methods
in Reinforcement Learning (RL). Leveraging duality, we propose a momentum-based
PMD update. By taking the functional route, our approach is independent of the
policy parametrization and applicable to large-scale optimization, covering
previous applications of momentum at the level of policy parameters as a
special case. We theoretically analyze several properties of this approach and
complement with a numerical ablation study, which serves to illustrate the
policy optimization dynamics on the value polytope, relative to different
algorithmic design choices in this space. We further characterize numerically
several features of the problem setting relevant for functional acceleration,
and lastly, we investigate the impact of approximation on their learning
mechanics.
