  Bayesian optimization (BO) is a class of global optimization algorithms,
suitable for minimizing an expensive objective function in as few function
evaluations as possible. While BO budgets are typically given in iterations,
this implicitly measures convergence in terms of iteration count and assumes
each evaluation has identical cost. In practice, evaluation costs may vary in
different regions of the search space. For example, the cost of neural network
training increases quadratically with layer size, which is a typical
hyperparameter. Cost-aware BO measures convergence with alternative cost
metrics such as time, energy, or money, for which vanilla BO methods are
unsuited. We introduce Cost Apportioned BO (CArBO), which attempts to minimize
an objective function in as little cost as possible. CArBO combines a
cost-effective initial design with a cost-cooled optimization phase which
depreciates a learned cost model as iterations proceed. On a set of 20
black-box function optimization problems we show that, given the same cost
budget, CArBO finds significantly better hyperparameter configurations than
competing methods.
