  Orthogonal greedy learning (OGL) is a stepwise learning scheme that adds a
new atom from a dictionary via the steepest gradient descent and build the
estimator via orthogonal projecting the target function to the space spanned by
the selected atoms in each greedy step. Here, "greed" means choosing a new atom
according to the steepest gradient descent principle. OGL then avoids the
overfitting/underfitting by selecting an appropriate iteration number. In this
paper, we point out that the overfitting/underfitting can also be avoided via
redefining "greed" in OGL. To this end, we introduce a new greedy metric,
called $\delta$-greedy thresholds, to refine "greed" and theoretically verifies
its feasibility. Furthermore, we reveals that such a greedy metric can bring an
adaptive termination rule on the premise of maintaining the prominent learning
performance of OGL. Our results show that the steepest gradient descent is not
the unique greedy metric of OGL and some other more suitable metric may lessen
the hassle of model-selection of OGL.
