## 1 Introduction  
Machine learning (ML) models have exploded in complexity in recent years at the expense of high computational costs [1]. ML is actually the calculation process of learning data through a certain algorithm. Parameters that can be updated during the training process are called model parameters. There is another kind of parameter, hyperparameter, which should be defined before training and cannot be learned from the normal training process. For instance, the kernel, regularization parameter, and kernel coefficient of a support vector machine (SVM), and the hidden state size and learning rate of a deep learning (DL) model are all hyperparameters. The process of finding the optimal hyperparameters is inevitable since hyperparameters have a remarkable effect on the performance in terms of time or accuracy of the model. In many cases, engineers rely on the trial-and-error method to manually tune hyperparameters. Even experienced engineers will try multiple times in a certain range to find the optimal combination of hyperparameters, not to mention that for non-experts in ML and DL, finding the best hyperparameters is time consuming and difficult. To solve this issue, automated ML (AutoML) has been proposed, which can build ML pipelines on a limited computational budget automatically, without human interference. The overall process of AutoML consists of four phases: data preparation, feature engineering, model generation, and model evaluation [2]. The optimization method is a part of model generation, which can be further divided into architecture optimization (AO) and hyperparameter optimization (HPO). [PERSON] et al. (2018) defined the automatic selection of learning algorithms and the setting of hyperparameters to optimize empirical performance as a combined algorithm selection and hyperparameter optimization (CASH) problem. In this work, we focus on the HPO task. In practice, HPO is confronted with many challenges, which make it a difficult problem. First, the hyperparameter tuning of ML models is generally considered a black-box optimization problem, that is, we can only observe the inputs and outputs of the model during the tuning process. We usually cannot obtain the gradient of the cost function with respect to the hyperparameters. Second, when facing large models, large datasets, the target model needs to be trained with selected hyperparameters to obtain the loss value, so the process of evaluation is very expensive. Finally, the configuration space is very complex and high dimensional. For a given algorithm, there are multiple hyperparameters correspondingly, and each hyperparameter has its own range of values. Recently, many methods are used to solve HPO problem, and several libraries have implemented these methods to allow researchers to conveniently work with them, such as Hyperopt ([[https://github.com/hyperopt/hyperopt](https://github.com/hyperopt/hyperopt)]([https://github.com/hyperopt/hyperopt](https://github.com/hyperopt/hyperopt)), accessed on 16 May 2022), HpBandSter ([[https://github.com/automl/HpBandSter](https://github.com/automl/HpBandSter)]([https://github.com/automl/HpBandSter](https://github.com/automl/HpBandSter)), accessed on 16 May 2022), SMAC ([[https://github.com/automl/SMAC3](https://github.com/automl/SMAC3)]([https://github.com/automl/SMAC3](https://github.com/automl/SMAC3)), accessed on 16 May 2022), Sherpa (2018), etc. The methods shown in Figure 1 are mainly classified into two categories:  
* Black-box optimization, e.g., grid search (GS) ([PERSON] and others, 2018), random search (RS) ([PERSON] and others, 2018), Bayesian optimization (BO) ([PERSON] and others, 2018; [PERSON] and others, 2018), simulated annealing (SA) ([PERSON] and others, 2018), and evolution algorithm (EA) ([PERSON] and others, 2018). * Multi-fidelity optimization, e.g., successive having (SH) ([PERSON] and others, 2018), hyperband ([PERSON] and others, 2018), Bayesian optimization hyperband (BOHB) ([PERSON] and others, 2018), and differential evolution hyperband (DEHB) ([PERSON] and others, 2018).