Learning and approximation capabilities of orthogonal super greedy algorithm

We consider the approximation capability of orthogonal super greedy algorithms (OSGA) and its applications in supervised learning. OSGA focuses on selecting more than one atoms in each iteration, which, of course, reduces the computational burden when compared with the conventional orthogonal greedy algorithm (OGA). We prove that even for function classes that are not the convex hull of the dictionary, OSGA does not degrade the approximation capability of OGA, provided the dictionary is incoherent. Based on this, we deduce tight generalization error bounds for OSGA learning. Our results show that in the realm of supervised learning, OSGA provides a possibility to further reduce the computational burden of OGA on the premise of maintaining its prominent generalization capability.