  An automatic machine learning (AutoML) task is to select the best algorithm
and its hyper-parameters simultaneously. Previously, the hyper-parameters of
all algorithms are joint as a single search space, which is not only huge but
also redundant, because many dimensions of hyper-parameters are irrelevant with
the selected algorithms. In this paper, we propose a cascaded approach for
algorithm selection and hyper-parameter optimization. While a search procedure
is employed at the level of hyper-parameter optimization, a bandit strategy
runs at the level of algorithm selection to allocate the budget based on the
search feedbacks. Since the bandit is required to select the algorithm with the
maximum performance, instead of the average performance, we thus propose the
extreme-region upper confidence bound (ER-UCB) strategy, which focuses on the
extreme region of the underlying feedback distribution. We show theoretically
that the ER-UCB has a regret upper bound $O\left(K \ln n\right)$ with
independent feedbacks, which is as efficient as the classical UCB bandit. We
also conduct experiments on a synthetic problem as well as a set of AutoML
tasks. The results verify the effectiveness of the proposed method.
