Yi-Shan Wu (Academia Sinica); Yi-Te Hong (Academia Sinica)*; Chi-Jen Lu (Academia Sinica)PMLR Page
The problem of branching experts is an extension of the experts problem where the set of experts may grow over time. We compare this problem in different learning settings along several axes: adversarial versus stochastic losses; a fixed versus a growing set of experts (branching experts); and single-task versus lifelong learning with expert advice. First, for the branching experts problem, we achieve tight regret bounds in both adversarial and stochastic setting with a single algorithm. While it was known that the adversarial branching experts problem is strictly harder than the non-branching one, the stochastic branching experts problem is in fact no harder. Next, we study the extension to the lifelong learning with expert advice in which one has to make online predictions with a sequence of tasks. For this problem, we provide a single algorithm which works for both adversarial and stochastic setting, and our bounds when specialized to the case without branching recover the regret bounds previously achieved separately via different algorithms. Furthermore, we prove a regret lower bound which shows that in the lifelong learning scenario, the case with branching experts now becomes strictly harder than the non-branching case in the stochastic setting.