  We study learning algorithms when there is a mismatch between the
distributions of the training and test datasets of a learning algorithm. The
effect of this mismatch on the generalization error and model misspecification
are quantified. Moreover, we provide a connection between the generalization
error and the rate-distortion theory, which allows one to utilize bounds from
the rate-distortion theory to derive new bounds on the generalization error and
vice versa. In particular, the rate-distortion based bound strictly improves
over the earlier bound by Xu and Raginsky even when there is no mismatch. We
also discuss how "auxiliary loss functions" can be utilized to obtain upper
bounds on the generalization error.
