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. We formalise this task as a \emph{multi-fidelity} bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop \mfgpucb, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour, and achieves better regret than strategies which ignore multi-fidelity information.

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.

Evolutionary neural architecture search (ENAS) has recently received increasing attention by effectively finding high-quality neural architectures, which however consumes high computational cost by training the architecture encoded by each individual for complete epochs in individual evaluation. Numerous ENAS approaches have been developed to reduce the evaluation cost, but it is often difficult for most of these approaches to achieve high evaluation accuracy. To address this issue, in this paper we propose an accelerated ENAS via multifidelity evaluation termed MFENAS, where the individual evaluation cost is significantly reduced by training the architecture encoded by each individual for only a small number of epochs. The balance between evaluation cost and evaluation accuracy is well maintained by suggesting a multi-fidelity evaluation, which identifies the potentially good individuals that cannot survive from previous generations by integrating multiple evaluations under different numbers of training epochs. For high diversity of neural architectures, a population initialization strategy is devised to produce different neural architectures varying from ResNet-like architectures to Inception-like ones. Experimental results on CIFAR-10 show that the architecture obtained by the proposed MFENAS achieves a 2.39% test error rate at the cost of only 0.6 GPU days on one NVIDIA 2080TI GPU, demonstrating the superiority of the proposed MFENAS over state-of-the-art NAS approaches in terms of both computational cost and architecture quality. The architecture obtained by the proposed MFENAS is then transferred to CIFAR-100 and ImageNet, which also exhibits competitive performance to the architectures obtained by existing NAS approaches. The source code of the proposed MFENAS is available at https://github.com/DevilYangS/MFENAS/.

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.