This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise. We consider the problem of finding the best interpolant from a class of kernels with unknown hyperparameters, assuming only that the noise is square-integrable. We provide finite-sample guarantees for the problem, characterizing how increasing the complexity of the kernel class increases the complexity of learning kernel hyperparameters. For common kernel classes (e.g. squared-exponential kernels with unknown lengthscale), our results show that hyperparameter optimization increases sample complexity by just a logarithmic factor, in comparison to the setting where optimal parameters are known in advance. Our result is based on a subsampling guarantee for linear regression under multiple design matrices, combined with an ε-net argument for discretizing kernel parameterizations.
Tuning hyperparameters for machine learning algorithms is a tedious task, one that is typically done manually. To enable automated hyperparameter tuning, recent works have started to use techniques based on Bayesian optimization. However, to practically enable automated tuning for large scale machine learning training pipelines, significant gaps remain in existing libraries, including lack of abstractions, fault tolerance, and flexibility to support scheduling on any distributed computing framework. To address these challenges, we present Mango, a Python library for parallel hyperparameter tun…
In this paper we develop a Bayesian optimization based hyperparameter tuning framework inspired by statistical learning theory for classifiers. We utilize two key facts from PAC learning theory; the generalization bound will be higher for a small subset of data compared to the whole, and the highest accuracy for a small subset of data can be achieved with a simple model. We initially tune the hyperparameters on a small subset of training data using Bayesian optimization. While tuning the hyperparameters on the whole training data, we leverage the insights from the learning theory to seek more …
Ludwig-Maximilians-Universität München（慕尼黑大学）；Fraunhofer Institute for Integrated Circuits IIS（弗劳恩霍夫集成电路研究所）
Both feature selection and hyperparameter tuning are key tasks in machine learning. Hyperparameter tuning is often useful to increase model performance, while feature selection is undertaken to attain sparse models. Sparsity may yield better model interpretability and lower cost of data acquisition, data handling and model inference. While sparsity may have a beneficial or detrimental effect on predictive performance, a small drop in performance may be acceptable in return for a substantial gain in sparseness. We therefore treat feature selection as a multi-objective optimization task. We perf…
Indian Institute of Management Ahmedabad（印度管理学院艾哈迈达巴德分校）
Hyperparameter tuning is an active area of research in machine learning, where the aim is to identify the optimal hyperparameters that provide the best performance on the validation set. Hyperparameter tuning is often achieved using naive techniques, such as random search and grid search. However, most of these methods seldom lead to an optimal set of hyperparameters and often get very expensive. In this paper, we propose a bilevel solution method for solving the hyperparameter optimization problem that does not suffer from the drawbacks of the earlier studies. The proposed method is general a…
With the surge in the number of hyperparameters and training times of modern machine learning models, hyperparameter tuning is becoming increasingly expensive. However, after assessing 40 tuning methods systematically, we find that each faces certain limitations. In particular, methods that speed up tuning via knowledge transfer typically require the final performance of hyperparameters and do not focus on low-fidelity information. As we demonstrate empirically, this common practice is suboptimal and can incur an unnecessary use of resources. It is more cost-efficient to instead leverage low-f…
The performance of deep (reinforcement) learning systems crucially depends on the choice of hyperparameters. Their tuning is notoriously expensive, typically requiring an iterative training process to run for numerous steps to convergence. Traditional tuning algorithms only consider the final performance of hyperparameters acquired after many expensive iterations and ignore intermediate information from earlier training steps. In this paper, we present a Bayesian optimization (BO) approach which exploits the iterative structure of learning algorithms for efficient hyperparameter tuning. We pro…
University of Málaga（马拉加大学）；Biomedic Research Institute of Málaga (IBIMA)（马拉加生物医学研究所 (IBIMA)）；University of Michigan（密歇根大学）
Support Vector Machines (SVMs) are still one of the most popular and precise classifiers. The Radial Basis Function (RBF) kernel has been used in SVMs to separate among classes with considerable success. However, there is an intrinsic dependence on the initial value of the kernel hyperparameter. In this work, we propose OKSVM, an algorithm that automatically learns the RBF kernel hyperparameter and adjusts the SVM weights simultaneously. The proposed optimization technique is based on a gradient descent method. We analyze the performance of our approach with respect to the classical SVM for cl…
École de Technologie Supérieure - Université du Québec（魁北克大学高等技术学院）；University of Santa Catarina（圣卡塔琳娜联邦大学）；Pontifícia Universidade Católica do Paraná（巴拉那天主教大学）
In this paper, we propose the use of a black-box optimization method called deterministic Mesh Adaptive Direct Search (MADS) algorithm with orthogonal directions (Ortho-MADS) for the selection of hyperparameters of Support Vector Machines with a Gaussian kernel. Different from most of the methods in the literature that exploit the properties of the data or attempt to minimize the accuracy of a validation dataset over the first quadrant of (C, gamma), the Ortho-MADS provides convergence proof. We present the MADS, followed by the Ortho-MADS, the dynamic stopping criterion defined by the MADS me…
University of New South Wales, Australia（新南威尔士大学，澳大利亚）
Deep learning algorithms have achieved excellent performance lately in a wide range of fields (e.g., computer version). However, a severe challenge faced by deep learning is the high dependency on hyper-parameters. The algorithm results may fluctuate dramatically under the different configuration of hyper-parameters. Addressing the above issue, this paper presents an efficient Orthogonal Array Tuning Method (OATM) for deep learning hyper-parameter tuning. We describe the OATM approach in five detailed steps and elaborate on it using two widely used deep neural network structures (Recurrent Neu…
ETH Zurich（苏黎世联邦理工学院）；University of Toronto（多伦多大学）
Bayesian optimization (BO) based on Gaussian process models is a powerful paradigm to optimize black-box functions that are expensive to evaluate. While several BO algorithms provably converge to the global optimum of the unknown function, they assume that the hyperparameters of the kernel are known in advance. This is not the case in practice and misspecification often causes these algorithms to converge to poor local optima. In this paper, we present the first BO algorithm that is provably no-regret and converges to the optimum without knowledge of the hyperparameters. During optimization we…
Tuning hyperparameters is a crucial but arduous part of the machine learning pipeline. Hyperparameter optimization is even more challenging in federated learning, where models are learned over a distributed network of heterogeneous devices; here, the need to keep data on device and perform local training makes it difficult to efficiently train and evaluate configurations. In this work, we investigate the problem of federated hyperparameter tuning. We first identify key challenges and show how standard approaches may be adapted to form baselines for the federated setting. Then, by making a nove…
Automated hyperparameter tuning aspires to facilitate the application of machine learning for non-experts. In the literature, different optimization approaches are applied for that purpose. This paper investigates the performance of Differential Evolution for tuning hyperparameters of supervised learning algorithms for classification tasks. This empirical study involves a range of different machine learning algorithms and datasets with various characteristics to compare the performance of Differential Evolution with Sequential Model-based Algorithm Configuration (SMAC), a reference Bayesian Op…
University of Texas at Austin（得克萨斯大学奥斯汀分校）；Alibaba US, Damo Academy（阿里巴巴美国达摩院）
Learned Iterative Shrinkage-Thresholding Algorithm (LISTA) introduces the concept of unrolling an iterative algorithm and training it like a neural network. It has had great success on sparse recovery. In this paper, we show that adding momentum to intermediate variables in the LISTA network achieves a better convergence rate and, in particular, the network with instance-optimal parameters is superlinearly convergent. Moreover, our new theoretical results lead to a practical approach of automatically and adaptively calculating the parameters of a LISTA network layer based on its previous layer…
Twitter（推特）；Facebook（脸书）；SigOpt, an Intel company（SigOpt（英特尔公司旗下））；Valohai；Paradigm（第四范式）；ChaLearn
This paper presents the results and insights from the black-box optimization (BBO) challenge at NeurIPS 2020 which ran from July-October, 2020. The challenge emphasized the importance of evaluating derivative-free optimizers for tuning the hyperparameters of machine learning models. This was the first black-box optimization challenge with a machine learning emphasis. It was based on tuning (validation set) performance of standard machine learning models on real datasets. This competition has widespread impact as black-box optimization (e.g., Bayesian optimization) is relevant for hyperparamete…
Bayesian optimization is popular for optimizing time-consuming black-box objectives. Nonetheless, for hyperparameter tuning in deep neural networks, the time required to evaluate the validation error for even a few hyperparameter settings remains a bottleneck. Multi-fidelity optimization promises relief using cheaper proxies to such objectives --- for example, validation error for a network trained using a subset of the training points or fewer iterations than required for convergence. We propose a highly flexible and practical approach to multi-fidelity Bayesian optimization, focused on effic…
University of Freiburg（弗赖堡大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Bayesian Optimization (BO) is a common approach for hyperparameter optimization (HPO) in automated machine learning. Although it is well-accepted that HPO is crucial to obtain well-performing machine learning models, tuning BO's own hyperparameters is often neglected. In this paper, we empirically study the impact of optimizing BO's own hyperparameters and the transferability of the found settings using a wide range of benchmarks, including artificial functions, HPO and HPO combined with neural architecture search. In particular, we show (i) that tuning can improve the any-time performance of …
Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model. Classically, these hyperparameters are optimized to minimize the prediction error of the model but this process totally neglects its later usage in the control loop. In this work, we present a framework to optimize the kernel and hyperparameters of a kernel-based model directly with respect to the closed-loop performance of the model. Our framework uses Bayesian …
Alleviating Hyperparameter-Tuning Burden in SVM Classifiers for Pulmonary Nodules Diagnosis with Multi-Task Bayesian Optimization
Yau Mathematical Sciences Center Tsinghua University（姚数学科学中心清华大学）；The First Affiliated Hospital of Guangzhou Medical University（广州医科大学第一附属医院）；China State Key Laboratory of Respiratory Disease（中国呼吸疾病国家重点实验室）；Academy of Mathematics and Systems Science Chinese Academy of Sciences（数学科学学院中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Thoracic Surgery and Oncology The First Affiliated Hospital of Guangzhou Medical University（胸外科与肿瘤科广州医科大学第一附属医院）
Bayesian Optimization for Hyperparameters Tuning in Neural Networks
Facoltà di Ingegneria dell’Informazione, Informatica e Statistica（信息、计算机与统计工程学院）；Dipartimento di Ingegneria Informatica, Automatica e Gestionale（信息、自动化与管理工程系）
Knight Foundation School of Computing and Information Sciences, Florida International University（佛罗里达国际大学奈特基金会计算与信息科学学院）；Sustainability, Optimization, and Learning for InterDependent networks (solid) laboratory, FIU（佛罗里达国际大学可持续性、优化与相互依赖网络学习实验室）；Department of Computer Science, University of Georgia（佐治亚大学计算机科学系）
Hyperparameter tuning in machine learning algorithms is a computationally challenging task due to the large-scale nature of the problem. In order to develop an efficient strategy for hyper-parameter tuning, one promising solution is to use swarm intelligence algorithms. Artificial Bee Colony (ABC) optimization lends itself as a promising and efficient optimization algorithm for this purpose. However, in some cases, ABC can suffer from a slow convergence rate or execution time due to the poor initial population of solutions and expensive objective functions. To address these concerns, a novel a…
University of Sydney（悉尼大学）；Data61, CSIRO（联邦科学与工业研究组织数据61研究所）；Australian National University（澳大利亚国立大学）
Conditional kernel mean embeddings are nonparametric models that encode conditional expectations in a reproducing kernel Hilbert space. While they provide a flexible and powerful framework for probabilistic inference, their performance is highly dependent on the choice of kernel and regularization hyperparameters. Nevertheless, current hyperparameter tuning methods predominantly rely on expensive cross validation or heuristics that is not optimized for the inference task. For conditional kernel mean embeddings with categorical targets and arbitrary inputs, we propose a hyperparameter learning …
Aalto University（阿尔托大学）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
Kernel functions are a powerful tool to enhance the $k$-means clustering algorithm via the kernel trick. It is known that the parameters of the chosen kernel function can have a dramatic impact on the result. In supervised settings, these can be tuned via cross-validation, but for clustering this is not straightforward and heuristics are usually employed. In this paper we study the impact of kernel parameters on kernel $k$-means. In particular, we derive a lower bound, tight up to constant factors, below which the parameter of the RBF kernel will render kernel $k$-means meaningless. We argue t…
Eindhoven University of Technology（埃因霍温理工大学）；Columbia University（哥伦比亚大学）
The performance of many machine learning algorithms depends on their hyperparameter settings. The goal of this study is to determine whether it is important to tune a hyperparameter or whether it can be safely set to a default value. We present a methodology to determine the importance of tuning a hyperparameter based on a non-inferiority test and tuning risk: the performance loss that is incurred when a hyperparameter is not tuned, but set to a default value. Because our methods require the notion of a default parameter, we present a simple procedure that can be used to determine reasonable d…
Università degli Studi di Genova（热那亚大学）；Massachusetts Institute of Technology（麻省理工学院）；Istituto Italiano di Tecnologia（意大利理工学院）
Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming of these solutions is that hyperparameter tuning is not taken care of, and left for the user to perform. Hyperparameters are crucial in practice and the lack of automated tuning greatly hinders efficiency and usability. In this paper, we work to fill in this gap focusing on kernel ridge regression based on the Nyström approximation. After reviewing and cont…
Carnegie Mellon University（卡内基梅隆大学）；Determined AI（Determined人工智能公司）；University of Washington（华盛顿大学）
Hyperparameter tuning of multi-stage pipelines introduces a significant computational burden. Motivated by the observation that work can be reused across pipelines if the intermediate computations are the same, we propose a pipeline-aware approach to hyperparameter tuning. Our approach optimizes both the design and execution of pipelines to maximize reuse. We design pipelines amenable for reuse by (i) introducing a novel hybrid hyperparameter tuning method called gridded random search, and (ii) reducing the average training time in pipelines by adapting early-stopping hyperparameter tuning app…
Idiap Research Institute（伊迪亚普研究所）；EPFL（洛桑联邦理工学院）；University of Geneva（日内瓦大学）
The performance of optimizers, particularly in deep learning, depends considerably on their chosen hyperparameter configuration. The efficacy of optimizers is often studied under near-optimal problem-specific hyperparameters, and finding these settings may be prohibitively costly for practitioners. In this work, we argue that a fair assessment of optimizers' performance must take the computational cost of hyperparameter tuning into account, i.e., how easy it is to find good hyperparameter configurations using an automatic hyperparameter search. Evaluating a variety of optimizers on an extensiv…
The performance of policy gradient methods is sensitive to hyperparameter settings that must be tuned for any new application. Widely used grid search methods for tuning hyperparameters are sample inefficient and computationally expensive. More advanced methods like Population Based Training that learn optimal schedules for hyperparameters instead of fixed settings can yield better results, but are also sample inefficient and computationally expensive. In this paper, we propose Hyperparameter Optimisation on the Fly (HOOF), a gradient-free algorithm that requires no more than one training run …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact be…
The random forest algorithm (RF) has several hyperparameters that have to be set by the user, e.g., the number of observations drawn randomly for each tree and whether they are drawn with or without replacement, the number of variables drawn randomly for each split, the splitting rule, the minimum number of samples that a node must contain and the number of trees. In this paper, we first provide a literature review on the parameters' influence on the prediction performance and on variable importance measures. It is well known that in most cases RF works reasonably well with the default values …
Penn State University（宾夕法尼亚州立大学）；UC Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Computational efficiency is an important consideration for deploying machine learning models for time series prediction in an online setting. Machine learning algorithms adjust model parameters automatically based on the data, but often require users to set additional parameters, known as hyperparameters. Hyperparameters can significantly impact prediction accuracy. Traffic measurements, typically collected online by sensors, are serially correlated. Moreover, the data distribution may change gradually. A typical adaptation strategy is periodically re-tuning the model hyperparameters, at the c…
Federal Technology University（联邦技术大学）；University of São Paulo（圣保罗大学）；Universidade Estadual Paulista（保利斯塔州立大学）；Eindhoven University of Technology（埃因霍温理工大学）
For many machine learning algorithms, predictive performance is critically affected by the hyperparameter values used to train them. However, tuning these hyperparameters can come at a high computational cost, especially on larger datasets, while the tuned settings do not always significantly outperform the default values. This paper proposes a recommender system based on meta-learning to identify exactly when it is better to use default values and when to tune hyperparameters for each new dataset. Besides, an in-depth analysis is performed to understand what they take into account for their d…
Tuning machine learning models at scale, especially finding the right hyperparameter values, can be difficult and time-consuming. In addition to the computational effort required, this process also requires some ancillary efforts including engineering tasks (e.g., job scheduling) as well as more mundane tasks (e.g., keeping track of the various parameters and associated results). We present Auptimizer, a general Hyperparameter Optimization (HPO) framework to help data scientists speed up model tuning and bookkeeping. With Auptimizer, users can use all available computing resources in distribut…
Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）；Google Research（谷歌研究院）；Determined AI；University of California, Berkeley（加利福尼亚大学伯克利分校）
Modern learning models are characterized by large hyperparameter spaces and long training times. These properties, coupled with the rise of parallel computing and the growing demand to productionize machine learning workloads, motivate the need to develop mature hyperparameter optimization functionality in distributed computing settings. We address this challenge by first introducing a simple and robust hyperparameter optimization algorithm called ASHA, which exploits parallelism and aggressive early-stopping to tackle large-scale hyperparameter optimization problems. Our extensive empirical r…
Amazon Web Services（亚马逊云科技）；University of Pennsylvania（宾夕法尼亚大学）；University of California, Los Angeles（加州大学洛杉矶分校）
Fine-tuning from pre-trained ImageNet models has become the de-facto standard for various computer vision tasks. Current practices for fine-tuning typically involve selecting an ad-hoc choice of hyperparameters and keeping them fixed to values normally used for training from scratch. This paper re-examines several common practices of setting hyperparameters for fine-tuning. Our findings are based on extensive empirical evaluation for fine-tuning on various transfer learning benchmarks. (1) While prior works have thoroughly investigated learning rate and batch size, momentum for fine-tuning is …
Institute for Data Science, Engineering, and Analytics（数据科学、工程与分析研究所）；Technische Hochschule Köln（科隆应用技术大学）
A surrogate model based hyperparameter tuning approach for deep learning is presented. This article demonstrates how the architecture-level parameters (hyperparameters) of deep learning models that were implemented in Keras/tensorflow can be optimized. The implementation of the tuning procedure is 100% accessible from R, the software environment for statistical computing. With a few lines of code, existing R packages (tfruns and SPOT) can be combined to perform hyperparameter tuning. An elementary hyperparameter tuning task (neural network and the MNIST data) is used to exemplify this approach
Machine learning algorithms such as random forests or xgboost are gaining more importance and are increasingly incorporated into production processes in order to enable comprehensive digitization and, if possible, automation of processes. Hyperparameters of these algorithms used have to be set appropriately, which can be referred to as hyperparameter tuning or optimization. Based on the concept of tunability, this article presents an overview of theoretical and practical results for popular machine learning algorithms. This overview is accompanied by an experimental analysis of 30 hyperparamet…
Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function
Université Grenoble Alpes, LJK, CNRS, Grenoble INP（格拉诺布尔大学，LJK，CNRS，格拉诺布尔INP）；Carnegie Mellon University, Machine Learning Department（卡内基梅隆大学，机器学习系）；Chinese University of Hong Kong, Department of Systems Engineering and Engineering Management（香港中文大学，系统工程与工程管理系）
The combined algorithm selection and hyperparameter tuning (CASH) problem is characterized by large hierarchical hyperparameter spaces. Model-free hyperparameter tuning methods can explore such large spaces efficiently since they are highly parallelizable across multiple machines. When no prior knowledge or meta-data exists to boost their performance, these methods commonly sample random configurations following a uniform distribution. In this work, we propose a novel sampling distribution as an alternative to uniform sampling and prove theoretically that it has a better chance of finding the …
Network embedding (NE) can generate succinct node representations for massive-scale networks and enable direct applications of common machine learning methods to the network structure. Various NE algorithms have been proposed and used in a number of applications, such as node classification and link prediction. NE algorithms typically contain hyperparameters that are key to performance, but the hyperparameter tuning process can be time consuming. It is desirable to have the hyperparameters tuned within a specified length of time. Although AutoML methods have been applied to the hyperparameter …
Bayesian optimization (BO) is a sample efficient approach to automatically tune the hyperparameters of machine learning models. In practice, one frequently has to solve similar hyperparameter tuning problems sequentially. For example, one might have to tune a type of neural network learned across a series of different classification problems. Recent work on multi-task BO exploits knowledge gained from previous tuning tasks to speed up a new tuning task. However, previous approaches do not account for the fact that BO is a sequential decision making procedure. Hence, there is in general a misma…
Hyperparameters in machine learning (ML) have received a fair amount of attention, and hyperparameter tuning has come to be regarded as an important step in the ML pipeline. But just how useful is said tuning? While smaller-scale experiments have been previously conducted, herein we carry out a large-scale investigation, specifically, one involving 26 ML algorithms, 250 datasets (regression and both binary and multinomial classification), 6 score metrics, and 28,857,600 algorithm runs. Analyzing the results we conclude that for many ML algorithms we should not expect considerable gains from hy…
We propose Bayesian extensions of two nonparametric regression methods which are kernel and mutual $k$-nearest neighbor regression methods. Derived based on Gaussian process models for regression, the extensions provide distributions for target value estimates and the framework to select the hyperparameters. It is shown that both the proposed methods asymptotically converge to kernel and mutual $k$-nearest neighbor regression methods, respectively. The simulation results show that the proposed methods can select proper hyperparameters and are better than or comparable to the former methods for…
Machine learning applications often require hyperparameter tuning. The hyperparameters usually drive both the efficiency of the model training process and the resulting model quality. For hyperparameter tuning, machine learning algorithms are complex black-boxes. This creates a class of challenging optimization problems, whose objective functions tend to be nonsmooth, discontinuous, unpredictably varying in computational expense, and include continuous, categorical, and/or integer variables. Further, function evaluations can fail for a variety of reasons including numerical difficulties or har…
University of Bath（巴斯大学）；Australian National University（澳大利亚国立大学）
Many machine learning solutions are framed as optimization problems which rely on good hyperparameters. Algorithms for tuning these hyperparameters usually assume access to exact solutions to the underlying learning problem, which is typically not practical. Here, we apply a recent dynamic accuracy derivative-free optimization method to hyperparameter tuning, which allows inexact evaluations of the learning problem while retaining convergence guarantees. We test the method on the problem of learning elastic net weights for a logistic classifier, and demonstrate its robustness and efficiency co…
