In-sample error and Max Likelihood

[hsolo]

The learning bounds we learnt in the course relate the generalization error of h, where h is the best hypothesis in terms of in-sample error, to the VC dimension.

In practice very often the best hypothesis h' is computed/estimated using Max Likelihood.

Is there a connection between the in-sample error of h' (the max likelihood hypothesis) and the minimum in-sample error possible?