  In a previous publication we proposed discrete global optimization as a
method to train a strong binary classifier constructed as a thresholded sum
over weak classifiers. Our motivation was to cast the training of a classifier
into a format amenable to solution by the quantum adiabatic algorithm. Applying
adiabatic quantum computing (AQC) promises to yield solutions that are superior
to those which can be achieved with classical heuristic solvers. Interestingly
we found that by using heuristic solvers to obtain approximate solutions we
could already gain an advantage over the standard method AdaBoost. In this
communication we generalize the baseline method to large scale classifier
training. By large scale we mean that either the cardinality of the dictionary
of candidate weak classifiers or the number of weak learners used in the strong
classifier exceed the number of variables that can be handled effectively in a
single global optimization. For such situations we propose an iterative and
piecewise approach in which a subset of weak classifiers is selected in each
iteration via global optimization. The strong classifier is then constructed by
concatenating the subsets of weak classifiers. We show in numerical studies
that the generalized method again successfully competes with AdaBoost. We also
provide theoretical arguments as to why the proposed optimization method, which
does not only minimize the empirical loss but also adds L0-norm regularization,
is superior to versions of boosting that only minimize the empirical loss. By
conducting a Quantum Monte Carlo simulation we gather evidence that the quantum
adiabatic algorithm is able to handle a generic training problem efficiently.
