  To attain the best learning accuracy, people move on with difficulties and
frustrations. Though one can optimize the empirical objective using a given set
of samples, its generalization ability to the entire sample distribution
remains questionable. Even if a fair generalization guarantee is offered, one
still wants to know what is to happen if the regularizer is removed, and/or how
well the artificial loss (like the hinge loss) relates to the accuracy.
  For such reason, this report surveys four different trials towards the
learning accuracy, embracing the major advances in supervised learning theory
in the past four years. Starting from the generic setting of learning, the
first two trials introduce the best optimization and generalization bounds for
convex learning, and the third trial gets rid of the regularizer. As an
innovative attempt, the fourth trial studies the optimization when the
objective is exactly the accuracy, in the special case of binary
classification. This report also analyzes the last trial through experiments.
