  In this work we consider the learning setting where, in addition to the
training set, the learner receives a collection of auxiliary hypotheses
originating from other tasks. We focus on a broad class of ERM-based linear
algorithms that can be instantiated with any non-negative smooth loss function
and any strongly convex regularizer. We establish generalization and excess
risk bounds, showing that, if the algorithm is fed with a good combination of
source hypotheses, generalization happens at the fast rate $\mathcal{O}(1/m)$
instead of the usual $\mathcal{O}(1/\sqrt{m})$. On the other hand, if the
source hypotheses combination is a misfit for the target task, we recover the
usual learning rate. As a byproduct of our study, we also prove a new bound on
the Rademacher complexity of the smooth loss class under weaker assumptions
compared to previous works.

Machine Learning