On the Theory of Transfer Learning: The Importance of Task Diversity

We provide new statistical guarantees for transfer learning via representation learning--when transfer is achieved by learning a feature representation shared across different tasks. This enables learning on new tasks using far less data than is required to learn them in isolation. Formally, we consider t+1 tasks parameterized by functions of the form fj circ h in a general function class F circ H, where each fj is a task-specific function in F and h is the shared representation in H. Letting C(·) denote the complexity measure of the function class, we show that for diverse training tasks (1) the sample complexity needed to learn the shared representation across the first t training tasks scales as C(H) + t C(F), despite no explicit access to a signal from the feature representation and (2) with an accurate estimate of the representation, the sample complexity needed to learn a new task scales only with C(F). Our results depend upon a new general notion of task diversity--applicable to models with general tasks, features, and losses--as well as a novel chain rule for Gaussian complexities. Finally, we exhibit the utility of our general framework in several models of importance in the literature.