  Lifelong learning can be viewed as a continuous transfer learning procedure
over consecutive tasks, where learning a given task depends on accumulated
knowledge --- the so-called knowledge base. Most published work on lifelong
learning makes a batch processing of each task, implying that a data collection
step is required beforehand. We are proposing a new framework, lifelong online
learning, in which the learning procedure for each task is interactive. This is
done through a computationally efficient algorithm where the predicted result
for a given task is made by combining two intermediate predictions: by using
only the information from the current task and by relying on the accumulated
knowledge. In this work, two challenges are tackled: making no assumption on
the task generation distribution, and processing with a possibly unknown number
of instances for each task. We are providing a theoretical analysis of this
algorithm, with a cumulative error upper bound for each task. We find that
under some mild conditions, the algorithm can still benefit from a small
cumulative error even when facing few interactions. Moreover, we provide
experimental results on both synthetic and real datasets that validate the
correct behavior and practical usefulness of the proposed algorithm.
