  Bayesian optimization (BO) is a popular method to optimize expensive
black-box functions. It efficiently tunes machine learning algorithms under the
implicit assumption that hyperparameter evaluations cost approximately the
same. In reality, the cost of evaluating different hyperparameters, be it in
terms of time, dollars or energy, can span several orders of magnitude of
difference. While a number of heuristics have been proposed to make BO
cost-aware, none of these have been proven to work robustly. In this work, we
reformulate cost-aware BO in terms of Pareto efficiency and introduce the cost
Pareto Front, a mathematical object allowing us to highlight the shortcomings
of commonly used acquisition functions. Based on this, we propose a novel
Pareto-efficient adaptation of the expected improvement. On 144 real-world
black-box function optimization problems we show that our Pareto-efficient
acquisition functions significantly outperform previous solutions, bringing up
to 50% speed-ups while providing finer control over the cost-accuracy
trade-off. We also revisit the common choice of Gaussian process cost models,
showing that simple, low-variance cost models predict training times
effectively.

Machine Learning;Machine Learning