Title: Bandit Optimisation with Approximations
Abstract:
In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function. Traditional methods for this problem assume just the availability of this single function. However, in many cases, cheap approximations may be available. For example, when tuning the hyper-parameters of an expensive statistical model via cross validation, we may choose to approximate the cross validation performance by training the model with subsets of the data and/or for a fewer number of iterations. We formalise this task as a multi-fidelity bandit problem where we may have access to either a finite number of approximations or a continuous spectrum of approximations to the target function. We develop upper confidence bound techniques assuming Gaussian process conditions on the target function and its approximations. We prove that our method uses the cheap approximations to eliminate low function value regions and deploys the expensive evaluations in a small region containing the optimum.
Preprints:
https://arxiv.org/abs/1610.09726
https://arxiv.org/abs/1603.06288
https://arxiv.org/abs/1703.06240