Regret Bounds for Lifelong Learning
This work addresses transfer learning for online sequential tasks, offering incremental improvements in regret bounds for specific applications like dictionary learning and predictor sets.
The paper tackles the problem of transfer learning in an online setting by proposing a lifelong learning strategy that refines data representations to transfer information between sequentially presented tasks, showing that it inherits regret bounds from within-task algorithms and improving bounds from O(1/√m) to O(1/m) for finite sets of predictors.
We consider the problem of transfer learning in an online setting. Different tasks are presented sequentially and processed by a within-task algorithm. We propose a lifelong learning strategy which refines the underlying data representation used by the within-task algorithm, thereby transferring information from one task to the next. We show that when the within-task algorithm comes with some regret bound, our strategy inherits this good property. Our bounds are in expectation for a general loss function, and uniform for a convex loss. We discuss applications to dictionary learning and finite set of predictors. In the latter case, we improve previous $O(1/\sqrt{m})$ bounds to $O(1/m)$ where $m$ is the per task sample size.