  Multi-objective Bayesian optimization aims to find the Pareto front of
optimal trade-offs between a set of expensive objectives while collecting as
few samples as possible. In some cases, it is possible to evaluate the
objectives separately, and a different latency or evaluation cost can be
associated with each objective. This presents an opportunity to learn the
Pareto front faster by evaluating the cheaper objectives more frequently. We
propose a scalarization based knowledge gradient acquisition function which
accounts for the different evaluation costs of the objectives. We prove
consistency of the algorithm and show empirically that it significantly
outperforms a benchmark algorithm which always evaluates both objectives.
