First of all, we thank all reviewers for their valuable time and feedback. We thank the reviewers for pointing out typos and grammatical errors, which we of course have fixed now. We are afraid that the reviewer might have misunderstood some parts of the paper. We refer to the original paper for further details about the approximation of the variational posterior. We have made this more clear in the main paper now.

Machine learning (ML) methods are used in most technical areas such as image recognition, product recommendation, financial analysis, medical diagnosis, and predictive maintenance. An important aspect of implementing ML methods involves controlling the learning process for the ML method so as to maximize the performance of the method under consideration. Hyperparameter tuning is the process of selecting a suitable set of ML method parameters that control its learning process. In this work, we demonstrate the use of discrete simulation optimization methods such as ranking and selection (R&S) and random search for identifying a hyperparameter set that maximizes the performance of a ML method. Specifically, we use the KN R&S method and the stochastic ruler random search method and one of its variations for this purpose. We also construct the theoretical basis for applying the KN method, which determines the optimal solution with a statistical guarantee via solution space enumeration. In comparison, the stochastic ruler method asymptotically converges to global optima and incurs smaller computational overheads. We demonstrate the application of these methods to a wide variety of machine learning models, including deep neural network models used for time series prediction and image classification. We benchmark our application of these methods with state-of-the-art hyperparameter optimization libraries such as $hyperopt$ and $mango$. The KN method consistently outperforms $hyperopt$'s random search (RS) and Tree of Parzen Estimators (TPE) methods. The stochastic ruler method outperforms the $hyperopt$ RS method and offers statistically comparable performance with respect to $hyperopt$'s TPE method and the $mango$ algorithm.

Hyperparameter optimization (HPO) is a well-studied research field. However, the effects and interactions of the components in an HPO pipeline are not yet well investigated. Then, we ask ourselves: Can the landscape of HPO be biased by the pipeline used to evaluate individual configurations? To address this question, we proposed to analyze the effect of the HPO pipeline on HPO problems using fitness landscape analysis. Particularly, we studied the DS-2019 HPO benchmark data set, looking for patterns that could indicate evaluation pipeline malfunction, and relate them to HPO performance. Our main findings are: (i) In most instances, large groups of diverse hyperparameters (i.e., multiple configurations) yield the same ill performance, most likely associated with majority class prediction models; (ii) in these cases, a worsened correlation between the observed fitness and average fitness in the neighborhood is observed, potentially making harder the deployment of local-search based HPO strategies. Finally, we concluded that the HPO pipeline definition might negatively affect the HPO landscape.

Hyperparameter optimization (HPO) is a key component of machine learning models for achieving peak predictive performance. While numerous methods and algorithms for HPO have been proposed over the last years, little progress has been made in illuminating and examining the actual structure of these black-box optimization problems. Exploratory landscape analysis (ELA) subsumes a set of techniques that can be used to gain knowledge about properties of unknown optimization problems. In this paper, we evaluate the performance of five different black-box optimizers on 30 HPO problems, which consist of two-, three- and five-dimensional continuous search spaces of the XGBoost learner trained on 10 different data sets. This is contrasted with the performance of the same optimizers evaluated on 360 problem instances from the black-box optimization benchmark (BBOB). We then compute ELA features on the HPO and BBOB problems and examine similarities and differences. A cluster analysis of the HPO and BBOB problems in ELA feature space allows us to identify how the HPO problems compare to the BBOB problems on a structural meta-level. We identify a subset of BBOB problems that are close to the HPO problems in ELA feature space and show that optimizer performance is comparably similar on these two sets of benchmark problems. We highlight open challenges of ELA for HPO and discuss potential directions of future research and applications.

When developing and analyzing new hyperparameter optimization (HPO) methods, it is vital to empirically evaluate and compare them on well-curated benchmark suites. In this work, we list desirable properties and requirements for such benchmarks and propose a new set of challenging and relevant multifidelity HPO benchmark problems motivated by these requirements. For this, we revisit the concept of surrogate-based benchmarks and empirically compare them to more widely-used tabular benchmarks, showing that the latter ones may induce bias in performance estimation and ranking of HPO methods. We present a new surrogate-based benchmark suite for multifidelity HPO methods consisting of 9 benchmark collections that constitute over 700 multifidelity HPO problems in total. All our benchmarks also allow for querying of multiple optimization targets, enabling the benchmarking of multi-objective HPO. We examine and compare our benchmark suite with respect to the defined requirements and show that our benchmarks provide viable additions to existing suites.

The Combined Algorithm Selection and Hyperparameter optimization (CASH) is one of the most fundamental problems in Automatic Machine Learning (AutoML). The existing Bayesian optimization (BO) based solutions turn the CASH problem into a Hyperparameter Optimization (HPO) problem by combining the hyperparameters of all machine learning (ML) algorithms, and use BO methods to solve it. As a result, these methods suffer from the low-efficiency problem due to the huge hyperparameter space in CASH. To alleviate this issue, we propose the alternating optimization framework, where the HPO problem for each ML algorithm and the algorithm selection problem are optimized alternately. In this framework, the BO methods are used to solve the HPO problem for each ML algorithm separately, incorporating a much smaller hyperparameter space for BO methods. Furthermore, we introduce Rising Bandits, a CASH-oriented Multi-Armed Bandits (MAB) variant, to model the algorithm selection in CASH. This framework can take the advantages of both BO in solving the HPO problem with a relatively small hyperparameter space and the MABs in accelerating the algorithm selection. Moreover, we further develop an efficient online algorithm to solve the Rising Bandits with provably theoretical guarantees. The extensive experiments on 30 OpenML datasets demonstrate the superiority of the proposed approach over the competitive baselines.

Machine learning algorithms have been used widely in various applications and areas. To fit a machine learning model into different problems, its hyper-parameters must be tuned. Selecting the best hyper-parameter configuration for machine learning models has a direct impact on the model's performance. It often requires deep knowledge of machine learning algorithms and appropriate hyper-parameter optimization techniques. Although several automatic optimization techniques exist, they have different strengths and drawbacks when applied to different types of problems. In this paper, optimizing the hyper-parameters of common machine learning models is studied. We introduce several state-of-the-art optimization techniques and discuss how to apply them to machine learning algorithms. Many available libraries and frameworks developed for hyper-parameter optimization problems are provided, and some open challenges of hyper-parameter optimization research are also discussed in this paper. Moreover, experiments are conducted on benchmark datasets to compare the performance of different optimization methods and provide practical examples of hyper-parameter optimization. This survey paper will help industrial users, data analysts, and researchers to better develop machine learning models by identifying the proper hyper-parameter configurations effectively.

The performance of deep neural networks is highly sensitive to the choice of the hyperparameters that define the structure of the network and the learning process. When facing a new application, tuning a deep neural network is a tedious and time consuming process that is often described as a "dark art". This explains the necessity of automating the calibration of these hyperparameters. Derivative-free optimization is a field that develops methods designed to optimize time consuming functions without relying on derivatives. This work introduces the HyperNOMAD package, an extension of the NOMAD software that applies the MADS algorithm [7] to simultaneously tune the hyperparameters responsible for both the architecture and the learning process of a deep neural network (DNN), and that allows for an important flexibility in the exploration of the search space by taking advantage of categorical variables. This new approach is tested on the MNIST and CIFAR-10 data sets and achieves results comparable to the current state of the art.