  In batch learning, stability together with existence and uniqueness of the
solution corresponds to well-posedness of Empirical Risk Minimization (ERM)
methods; recently, it was proved that CV_loo stability is necessary and
sufficient for generalization and consistency of ERM. In this note, we
introduce CV_on stability, which plays a similar note in online learning. We
show that stochastic gradient descent (SDG) with the usual hypotheses is CVon
stable and we then discuss the implications of CV_on stability for convergence
of SGD.
