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 cost of computational burden. In this work, we present an efficient and principled online hyperparameter optimization algorithm for Kernel Ridge regression applied to traffic prediction problems. In tests with real traffic measurement data, our approach requires as little as one-seventh of the computation time of other tuning methods, while achieving better or similar prediction accuracy.
Much of the work in metalearning has focused on classifier selection, combined more recently with hyperparameter optimization, with little concern for data preprocessing. Yet, it is generally well accepted that machine learning applications require not only model building, but also data preprocessing. In other words, practical solutions consist of pipelines of machine learning operators rather than single algorithms. Interestingly, our experiments suggest that, on average, data preprocessing hinders accuracy, while the best performing pipelines do actually make use of preprocessors. Here, we conduct an extensive empirical study over a wide range of learning algorithms and preprocessors, and use metalearning to determine when one should make use of preprocessors in ML pipeline design.
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 results show that ASHA outperforms existing state-of-the-art hyperparameter optimization methods; scales linearly with the number of workers in distributed settings; and is suitable for massive parallelism, as demonstrated on a task with 500 workers. We then describe several design decisions we encountered, along with our associated solutions, when integrating ASHA in Determined AI's end-to-end production-quality machine learning system that offers hyperparameter tuning as a service.
Many hyperparameter optimization (HyperOpt) methods assume restricted computing resources and mainly focus on enhancing performance. Here we propose a novel cloud-based HyperOpt (CHOPT) framework which can efficiently utilize shared computing resources while supporting various HyperOpt algorithms. We incorporate convenient web-based user interfaces, visualization, and analysis tools, enabling users to easily control optimization procedures and build up valuable insights with an iterative analysis procedure. Furthermore, our framework can be incorporated with any cloud platform, thus complementarily increasing the efficiency of conventional deep learning frameworks. We demonstrate applications of CHOPT with tasks such as image recognition and question-answering, showing that our framework can find hyperparameter configurations competitive with previous work. We also show CHOPT is capable of providing interesting observations through its analysing tools
Many different machine learning algorithms exist; taking into account each algorithm's hyperparameters, there is a staggeringly large number of possible alternatives overall. We consider the problem of simultaneously selecting a learning algorithm and setting its hyperparameters, going beyond previous work that addresses these issues in isolation. We show that this problem can be addressed by a fully automated approach, leveraging recent innovations in Bayesian optimization. Specifically, we consider a wide range of feature selection techniques (combining 3 search and 8 evaluator methods) and all classification approaches implemented in WEKA, spanning 2 ensemble methods, 10 meta-methods, 27 base classifiers, and hyperparameter settings for each classifier. On each of 21 popular datasets from the UCI repository, the KDD Cup 09, variants of the MNIST dataset and CIFAR-10, we show classification performance often much better than using standard selection/hyperparameter optimization methods. We hope that our approach will help non-expert users to more effectively identify machine learning algorithms and hyperparameter settings appropriate to their applications, and hence to achieve improved performance.
AutoML serves as the bridge between varying levels of expertise when designing machine learning systems and expedites the data science process. A wide range of techniques is taken to address this, however there does not exist an objective comparison of these techniques. We present a benchmark of current open source AutoML solutions using open source datasets. We test auto-sklearn, TPOT, auto_ml, and H2O's AutoML solution against a compiled set of regression and classification datasets sourced from OpenML and find that auto-sklearn performs the best across classification datasets and TPOT performs the best across regression datasets.
Hyperparameter tuning is the black art of automatically finding a good combination of control parameters for a data miner. While widely applied in empirical Software Engineering, there has not been much discussion on which hyperparameter tuner is best for software analytics. To address this gap in the literature, this paper applied a range of hyperparameter optimizers (grid search, random search, differential evolution, and Bayesian optimization) to defect prediction problem. Surprisingly, no hyperparameter optimizer was observed to be `best' and, for one of the two evaluation measures studied here (F-measure), hyperparameter optimization, in 50\% cases, was no better than using default configurations. We conclude that hyperparameter optimization is more nuanced than previously believed. While such optimization can certainly lead to large improvements in the performance of classifiers used in software analytics, it remains to be seen which specific optimizers should be applied to a new dataset.
Most learning algorithms require the practitioner to manually set the values of many hyperparameters before the learning process can begin. However, with modern algorithms, the evaluation of a given hyperparameter setting can take a considerable amount of time and the search space is often very high-dimensional. We suggest using a lower-dimensional representation of the original data to quickly identify promising areas in the hyperparameter space. This information can then be used to initialize the optimization algorithm for the original, higher-dimensional data. We compare this approach with the standard procedure of optimizing the hyperparameters only on the original input. We perform experiments with various state-of-the-art hyperparameter optimization algorithms such as random search, the tree of parzen estimators (TPEs), sequential model-based algorithm configuration (SMAC), and a genetic algorithm (GA). Our experiments indicate that it is possible to speed up the optimization process by using lower-dimensional data representations at the beginning, while increasing the dimensionality of the input later in the optimization process. This is independent of the underlying optimization procedure, making the approach promising for many existing hyperparameter optimization algorithms.
Modern machine learning algorithms are increasingly computationally demanding, requiring specialized hardware and distributed computation to achieve high performance in a reasonable time frame. Many hyperparameter search algorithms have been proposed for improving the efficiency of model selection, however their adaptation to the distributed compute environment is often ad-hoc. We propose Tune, a unified framework for model selection and training that provides a narrow-waist interface between training scripts and search algorithms. We show that this interface meets the requirements for a broad range of hyperparameter search algorithms, allows straightforward scaling of search to large clusters, and simplifies algorithm implementation. We demonstrate the implementation of several state-of-the-art hyperparameter search algorithms in Tune. Tune is available at http://ray.readthedocs.io/en/latest/tune.html.
Automatic machine learning performs predictive modeling with high performing machine learning tools without human interference. This is achieved by making machine learning applications parameter-free, i.e. only a dataset is provided while the complete model selection and model building process is handled internally through (often meta) optimization. Projects like Auto-WEKA and auto-sklearn aim to solve the Combined Algorithm Selection and Hyperparameter optimization (CASH) problem resulting in huge configuration spaces. However, for most real-world applications, the optimization over only a few different key learning algorithms can not only be sufficient, but also potentially beneficial. The latter becomes apparent when one considers that models have to be validated, explained, deployed and maintained. Here, less complex model are often preferred, for validation or efficiency reasons, or even a strict requirement. Automatic gradient boosting simplifies this idea one step further, using only gradient boosting as a single learning algorithm in combination with model-based hyperparameter tuning, threshold optimization and encoding of categorical features. We introduce this general framework as well as a concrete implementation called autoxgboost. It is compared to current AutoML projects on 16 datasets and despite its simplicity is able to achieve comparable results on about half of the datasets as well as performing best on two.
Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.
Modern deep learning methods are very sensitive to many hyperparameters, and, due to the long training times of state-of-the-art models, vanilla Bayesian hyperparameter optimization is typically computationally infeasible. On the other hand, bandit-based configuration evaluation approaches based on random search lack guidance and do not converge to the best configurations as quickly. Here, we propose to combine the benefits of both Bayesian optimization and bandit-based methods, in order to achieve the best of both worlds: strong anytime performance and fast convergence to optimal configurations. We propose a new practical state-of-the-art hyperparameter optimization method, which consistently outperforms both Bayesian optimization and Hyperband on a wide range of problem types, including high-dimensional toy functions, support vector machines, feed-forward neural networks, Bayesian neural networks, deep reinforcement learning, and convolutional neural networks. Our method is robust and versatile, while at the same time being conceptually simple and easy to implement.
Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of thumb, or sometimes brute-force search. Much more appealing is the idea of developing automatic approaches which can optimize the performance of a given learning algorithm to the task at hand. In this work, we consider the automatic tuning problem within the framework of Bayesian optimization, in which a learning algorithm's generalization performance is modeled as a sample from a Gaussian process (GP). The tractable posterior distribution induced by the GP leads to efficient use of the information gathered by previous experiments, enabling optimal choices about what parameters to try next. Here we show how the effects of the Gaussian process prior and the associated inference procedure can have a large impact on the success or failure of Bayesian optimization. We show that thoughtful choices can lead to results that exceed expert-level performance in tuning machine learning algorithms. We also describe new algorithms that take into account the variable cost (duration) of learning experiments and that can leverage the presence of multiple cores for parallel experimentation. We show that these proposed algorithms improve on previous automatic procedures and can reach or surpass human expert-level optimization on a diverse set of contemporary algorithms including latent Dirichlet allocation, structured SVMs and convolutional neural networks.
We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences.
One of the goals of the ICML workshop on representation and learning is to establish benchmark scores for a new data set of labeled facial expressions. This paper presents the performance of a "Null" model consisting of convolutions with random weights, PCA, pooling, normalization, and a linear readout. Our approach focused on hyperparameter optimization rather than novel model components. On the Facial Expression Recognition Challenge held by the Kaggle website, our hyperparameter optimization approach achieved a score of 60% accuracy on the test data. This paper also introduces a new ensemble construction variant that combines hyperparameter optimization with the construction of ensembles. This algorithm constructed an ensemble of four models that scored 65.5% accuracy. These scores rank 12th and 5th respectively among the 56 challenge participants. It is worth noting that our approach was developed prior to the release of the data set, and applied without modification; our strong competition performance suggests that the TPE hyperparameter optimization algorithm and domain expertise encoded in our Null model can generalize to new image classification data sets.
The identification of performance-optimizing parameter settings is an important part of the development and application of algorithms. We describe an automatic framework for this algorithm configuration problem. More formally, we provide methods for optimizing a target algorithm's performance on a given class of problem instances by varying a set of ordinal and/or categorical parameters. We review a family of local-search-based algorithm configuration procedures and present novel techniques for accelerating them by adaptively limiting the time spent for evaluating individual configurations. We describe the results of a comprehensive experimental evaluation of our methods, based on the configuration of prominent complete and incomplete algorithms for SAT. We also present what is, to our knowledge, the first published work on automatically configuring the CPLEX mixed integer programming solver. All the algorithms we considered had default parameter settings that were manually identified with considerable effort. Nevertheless, using our automated algorithm configuration procedures, we achieved substantial and consistent performance improvements.
BayesOpt is a library with state-of-the-art Bayesian optimization methods to solve nonlinear optimization, stochastic bandits or sequential experimental design problems. Bayesian optimization is sample efficient by building a posterior distribution to capture the evidence and prior knowledge for the target function. Built in standard C++, the library is extremely efficient while being portable and flexible. It includes a common interface for C, C++, Python, Matlab and Octave.
Optunity is a free software package dedicated to hyperparameter optimization. It contains various types of solvers, ranging from undirected methods to direct search, particle swarm and evolutionary optimization. The design focuses on ease of use, flexibility, code clarity and interoperability with existing software in all machine learning environments. Optunity is written in Python and contains interfaces to environments such as R and MATLAB. Optunity uses a BSD license and is freely available online at http://www.optunity.net.
Motivated by the task of hyperparameter optimization, we introduce the non-stochastic best-arm identification problem. Within the multi-armed bandit literature, the cumulative regret objective enjoys algorithms and analyses for both the non-stochastic and stochastic settings while to the best of our knowledge, the best-arm identification framework has only been considered in the stochastic setting. We introduce the non-stochastic setting under this framework, identify a known algorithm that is well-suited for this setting, and analyze its behavior. Next, by leveraging the iterative nature of standard machine learning algorithms, we cast hyperparameter optimization as an instance of non-stochastic best-arm identification, and empirically evaluate our proposed algorithm on this task. Our empirical results show that, by allocating more resources to promising hyperparameter settings, we typically achieve comparable test accuracies an order of magnitude faster than baseline methods.
The apsis toolkit presented in this paper provides a flexible framework for hyperparameter optimization and includes both random search and a bayesian optimizer. It is implemented in Python and its architecture features adaptability to any desired machine learning code. It can easily be used with common Python ML frameworks such as scikit-learn. Published under the MIT License other researchers are heavily encouraged to check out the code, contribute or raise any suggestions. The code can be found at github.com/FrederikDiehl/apsis.