Anastasia Pentina, Christoph H. Lampert
In this work we aim at extending theoretical foundations of lifelong learning. Previous work analyzing this scenario is based on the assumption that the tasks are sampled i.i.d. from a task environment or limited to strongly constrained data distributions. Instead we study two scenarios when lifelong learning is possible, even though the observed tasks do not form an i.i.d. sample: first, when they are sampled from the same environment, but possibly with dependencies, and second, when the task environment is allowed to change over time. In the first case we prove a PAC-Bayesian theorem, which can be seen as a direct generalization of the analogous previous result for the i.i.d. case. For the second scenario we propose to learn an inductive bias in form of a transfer procedure. We present a generalization bound and show on a toy example how it can be used to identify a beneficial transfer algorithm.