Before revision:  Our learning rates demonstrate consistency of the sample estimator under drastically weaker assumptions than the state-of-the art, allowing the much broader application of conditional mean embeddings to more complex ML/RL settings involving infinite dimensional RKHS and continuous state spaces.
After revision:  We derive explicit, adaptive convergence rates for the sample estimator under drastically weaker assumptions than the state-of-the art, allowing the much broader application of conditional mean embeddings to more complex ML/RL settings involving infinite dimensional RKHS and continuous state spaces.