Abstract: Most generalization bounds in learning theory are based on some measure of the complexity of the hypothesis class used, independently of any algorithm. In contrast, the notion of algorithmic stability can be used to derive tight generalization bounds that are tailored to specific learning algorithms by exploiting their particular properties. However, as in much of learning theory, existing stability analyses and bounds apply only in the scenario where the samples are independently and identically distributed. In many machine learning applications, however, this assumption does not hold. The observations received by the learning algorithm often have some inherent temporal dependence.