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:  Our learning rates demonstrate consistency of the sample estimator under the misspecifed setting, where the target operator is not Hilbert-Schmidt or bounded with respect to the input/output RKHSs. We demonstrate that in certain parameter regimes, we can achieve uniform convergence rates in the output RKHS. We hope our analyses will allow the much broader application of conditional mean embeddings to more complex ML/RL settings involving infinite dimensional RKHS and continuous state spaces.