Gaussian Process Bandit Optimisation with Multi-fidelity Evaluations

In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function \func . Traditional methods for this problem assume just the availability of this single function. However, in many cases, cheap approximations to \func may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of \func in a small but promising region and speedily identify the optimum.