  A new gradient-based optimization approach by automatically scheduling the
learning rate has been proposed recently, which is called Binary Forward
Exploration (BFE). The Adaptive version of BFE has also been discussed
thereafter. In this paper, the improved algorithms based on them will be
investigated, in order to optimize the efficiency and robustness of the new
methodology. This improved approach provides a new perspective to scheduling
the update of learning rate and will be compared with the stochastic gradient
descent, aka SGD algorithm with momentum or Nesterov momentum and the most
successful adaptive learning rate algorithm e.g. Adam. The goal of this method
does not aim to beat others but provide a different viewpoint to optimize the
gradient descent process. This approach combines the advantages of the
first-order and second-order optimizations in the aspects of speed and
efficiency.
