This NVIDIA post goes into extending Bayesian Optimization to multiple metrics [0]. It shows how you can use efficient optimization to find a good Pareto Frontier[1].

[0]: https://devblogs.nvidia.com/sigopt-deep-learning-hyperparame...

[1]: https://en.wikipedia.org/wiki/Pareto_efficiency

Thanks. What's DFO? And what do you usefully do with multiple objectives, besides minimise some total?

DFO is derivative free optimization. With multiple objectives you try to find different solutions given different weightings to the objectives for the Pareto front and pick one depending on the domain.