In this work we consider the learning setting where in addition to the training set, the learner receives a collection of auxiliary hypotheses originating from other tasks. This paradigm, known as Hypothesis Transfer Learning (HTL), has been successfully exploited in empirical works, but only recently has received a theoretical attention. Here, we try to understand when HTL facilitates accelerated generalization -- the goal of the transfer learning paradigm. Thus, we study a broad class of algorithms, a Hypothesis Transfer Learning through Regularized ERM, that can be instantiated with any non-negative smooth loss function and any strongly convex regularizer. We establish generalization and excess risk bounds, showing that if the algorithm is fed with a good source hypotheses combination, generalization happens at the fast rate $\mathcal{O}(1/m)$ instead of usual $\mathcal{O}(1/\sqrt{m})$. We also observe that if the combination is perfect, our theory formally backs up the intuition that learning is not necessary. On the other hand, if the source hypotheses combination is a misfit for the target task, we recover the usual learning rate. As a byproduct of our study, we also prove a new bound on the Rademacher complexity of the smooth loss class under weaker assumptions compared to previous works.

通过使用其他任务的假设集合，研究了一种广泛的以ERM为基础的线性算法，当传递的源假设组合适当时，证明了其具有加速收敛的泛化和过度风险的边界，然而，如果源假设组合不适合目标任务，那么它会恢复到常规的学习速率。

通过辅助假设的转移实现快速收敛