Learning capability of relaxed greedy algorithms

In the practice of machine learning, one often encounters problems in which noisy data are abundant while the learning targets are imprecise and elusive. To these challenges, most of the traditional learning algorithms employ hypothesis spaces of large capacity. This has inevitably led to high computational burdens and caused considerable machine sluggishness. Utilizing greedy algorithms in this kind of learning environment has greatly improved machine performance. The best existing learning rate of various greedy algorithms is proved to achieve the order of (m/log m)^-1/2, where $m$ is the sample size. In this paper, we provide a relaxed greedy algorithm and study its learning capability. We prove that the learning rate of the new relaxed greedy algorithm is faster than the order m^-1/2. Unlike many other greedy algorithms, which are often indecisive issuing a stopping order to the iteration process, our algorithm has a clearly established stopping criteria.