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We develop novel learning rates for conditional mean embeddings by applyingthe theory of interpolation for reproducing kernel Hilbert spaces (RKHS). Wederive explicit, adaptive convergence rates for the sample estimator under themisspecifed setting, where the target operator is not Hilbert-Schmidt orbounded with respect to the input/output RKHSs. We demonstrate that in certainparameter regimes, we can achieve uniform convergence rates in the output RKHS.We hope our analyses will allow the much broader application of conditionalmean embeddings to more complex ML/RL settings involving infinite dimensionalRKHSs and continuous state spaces.

Sobolev Norm Learning Rates for Conditional Mean Embeddings