Below is a theorem from the book "Foundations of Machine Learning".
It specifies the generalization bounds for Kernel Ridge Regression by making use of the Rademacher Complexity on linear models. $R(h)$ is the generalization error, and $\hat{R}(h)$ is the empirical error. Now pretty much everything is either known to us, picked by us, or can be calculated by us. $m$ is the number of training samples.
Instead of finding the right penalty $\Lambda$ via cross validation, can we simply pick the $\Lambda$ that minimizes the right hand side of the inequality? What should be the $\delta$ value to be set in order to achieve best predictive result? How to choose $r$ as tight as possible?
Is this an alternative to Cross Validation for Kernel Ridge (or just Ridge) Regression?