Due to the high computational demands executing a rigorous comparison between hyperparameter optimization (HPO) methods is often cumbersome. The goal of this paper is to facilitate a better empirical evaluation of HPO methods by providing benchmarks that are cheap to evaluate, but still represent realistic use cases. We believe these benchmarks provide an easy and efficient way to conduct reproducible experiments for neural hyperparameter search. Our benchmarks consist of a large grid of configurations of a feed forward neural network on four different regression datasets including architectural hyperparameters and hyperparameters concerning the training pipeline. Based on this data, we performed an in-depth analysis to gain a better understanding of the properties of the optimization problem, as well as of the importance of different types of hyperparameters. Second, we exhaustively compared various different state-of-the-art methods from the hyperparameter optimization literature on these benchmarks in terms of performance and robustness.
Neural Architecture Search (NAS) has been a source of dramatic improvements in neural network design, with recent results meeting or exceeding the performance of hand-tuned architectures. However, our understanding of how to represent the search space for neural net architectures and how to search that space efficiently are both still in their infancy. We have performed an in-depth analysis to identify limitations in a widely used search space and a recent architecture search method, Differentiable Architecture Search (DARTS). These findings led us to introduce novel network blocks with a more general, balanced, and consistent design; a better-optimized Cosine Power Annealing learning rate schedule; and other improvements. Our resulting sharpDARTS search is 50% faster with a 20-30% relative improvement in final model error on CIFAR-10 when compared to DARTS. Our best single model run has 1.93% (1.98+/-0.07) validation error on CIFAR-10 and 5.5% error (5.8+/-0.3) on the recently released CIFAR-10.1 test set. To our knowledge, both are state of the art for models of similar size. This model also generalizes competitively to ImageNet at 25.1% top-1 (7.8% top-5) error. We found improvements for existing search spaces but does DARTS generalize to new domains? We propose Differentiable Hyperparameter Grid Search and the HyperCuboid search space, which are representations designed to leverage DARTS for more general parameter optimization. Here we find that DARTS fails to generalize when compared against a human's one shot choice of models. We look back to the DARTS and sharpDARTS search spaces to understand why, and an ablation study reveals an unusual generalization gap. We finally propose Max-W regularization to solve this problem, which proves significantly better than the handmade design. Code will be made available.
We consider the problem of learning a binary classifier from only positive and unlabeled observations (called PU learning). Recent studies in PU learning have shown superior performance theoretically and empirically. However, most existing algorithms may not be suitable for large-scale datasets because they face repeated computations of a large Gram matrix or require massive hyperparameter optimization. In this paper, we propose a computationally efficient and theoretically grounded PU learning algorithm. The proposed PU learning algorithm produces a closed-form classifier when the hypothesis space is a closed ball in reproducing kernel Hilbert space. In addition, we establish upper bounds of the estimation error and the excess risk. The obtained estimation error bound is sharper than existing results and the derived excess risk bound has an explicit form, which vanishes as sample sizes increase. Finally, we conduct extensive numerical experiments using both synthetic and real datasets, demonstrating improved accuracy, scalability, and robustness of the proposed algorithm.
This paper investigates lung nodule classification by using deep neural networks (DNNs). Hyperparameter optimization in DNNs is a computationally expensive problem, where evaluating a hyperparameter configuration may take several hours or even days. Bayesian optimization has been recently introduced for the automatically searching of optimal hyperparameter configurations of DNNs. It applies probabilistic surrogate models to approximate the validation error function of hyperparameter configurations, such as Gaussian processes, and reduce the computational complexity to a large extent. However, most existing surrogate models adopt stationary covariance functions to measure the difference between hyperparameter points based on spatial distance without considering its spatial locations. This distance-based assumption together with the condition of constant smoothness throughout the whole hyperparameter search space clearly violates the property that the points far away from optimal points usually get similarly poor performance even though each two of them have huge spatial distance between them. In this paper, a non-stationary kernel is proposed which allows the surrogate model to adapt to functions whose smoothness varies with the spatial location of inputs, and a multi-level convolutional neural network (ML-CNN) is built for lung nodule classification whose hyperparameter configuration is optimized by using the proposed non-stationary kernel based Gaussian surrogate model. Our algorithm searches the surrogate for optimal setting via hyperparameter importance based evolutionary strategy, and the experiments demonstrate our algorithm outperforms manual tuning and well-established hyperparameter optimization methods such as Random search, Gaussian processes with stationary kernels, and recently proposed Hyperparameter Optimization via RBF and Dynamic coordinate search.
Transfer learning is one of the subjects undergoing intense study in the area of machine learning. In object recognition and object detection there are known experiments for the transferability of parameters, but not for neural networks which are suitable for object detection in real time embedded applications, such as the SqueezeDet neural network. We use transfer learning to accelerate the training of SqueezeDet to a new group of classes. Also, experiments are conducted to study the transferability and co-adaptation phenomena introduced by the transfer learning process. To accelerate training, we propose a new implementation of the SqueezeDet training which provides a faster pipeline for data processing and achieves 1.8 times speedup compared to the initial implementation. Finally, we created a mechanism for automatic hyperparameter optimization using an empirical method.
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.
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.
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.
Tuning hyperparameters of learning algorithms is hard because gradients are usually unavailable. We compute exact gradients of cross-validation performance with respect to all hyperparameters by chaining derivatives backwards through the entire training procedure. These gradients allow us to optimize thousands of hyperparameters, including step-size and momentum schedules, weight initialization distributions, richly parameterized regularization schemes, and neural network architectures. We compute hyperparameter gradients by exactly reversing the dynamics of stochastic gradient descent with momentum.
Over the past decade, data science and machine learning has grown from a mysterious art form to a staple tool across a variety of fields in academia, business, and government. In this paper, we introduce the concept of tree-based pipeline optimization for automating one of the most tedious parts of machine learning---pipeline design. We implement a Tree-based Pipeline Optimization Tool (TPOT) and demonstrate its effectiveness on a series of simulated and real-world genetic data sets. In particular, we show that TPOT can build machine learning pipelines that achieve competitive classification accuracy and discover novel pipeline operators---such as synthetic feature constructors---that significantly improve classification accuracy on these data sets. We also highlight the current challenges to pipeline optimization, such as the tendency to produce pipelines that overfit the data, and suggest future research paths to overcome these challenges. As such, this work represents an early step toward fully automating machine learning pipeline design.
As the field of data science continues to grow, there will be an ever-increasing demand for tools that make machine learning accessible to non-experts. In this paper, we introduce the concept of tree-based pipeline optimization for automating one of the most tedious parts of machine learning---pipeline design. We implement an open source Tree-based Pipeline Optimization Tool (TPOT) in Python and demonstrate its effectiveness on a series of simulated and real-world benchmark data sets. In particular, we show that TPOT can design machine learning pipelines that provide a significant improvement over a basic machine learning analysis while requiring little to no input nor prior knowledge from the user. We also address the tendency for TPOT to design overly complex pipelines by integrating Pareto optimization, which produces compact pipelines without sacrificing classification accuracy. As such, this work represents an important step toward fully automating machine learning pipeline design.
Hyperparameter selection generally relies on running multiple full training trials, with selection based on validation set performance. We propose a gradient-based approach for locally adjusting hyperparameters during training of the model. Hyperparameters are adjusted so as to make the model parameter gradients, and hence updates, more advantageous for the validation cost. We explore the approach for tuning regularization hyperparameters and find that in experiments on MNIST, SVHN and CIFAR-10, the resulting regularization levels are within the optimal regions. The additional computational cost depends on how frequently the hyperparameters are trained, but the tested scheme adds only 30% computational overhead regardless of the model size. Since the method is significantly less computationally demanding compared to similar gradient-based approaches to hyperparameter optimization, and consistently finds good hyperparameter values, it can be a useful tool for training neural network models.
Most models in machine learning contain at least one hyperparameter to control for model complexity. Choosing an appropriate set of hyperparameters is both crucial in terms of model accuracy and computationally challenging. In this work we propose an algorithm for the optimization of continuous hyperparameters using inexact gradient information. An advantage of this method is that hyperparameters can be updated before model parameters have fully converged. We also give sufficient conditions for the global convergence of this method, based on regularity conditions of the involved functions and summability of errors. Finally, we validate the empirical performance of this method on the estimation of regularization constants of L2-regularized logistic regression and kernel Ridge regression. Empirical benchmarks indicate that our approach is highly competitive with respect to state of the art methods.
Bayesian optimization has become a successful tool for hyperparameter optimization of machine learning algorithms, such as support vector machines or deep neural networks. Despite its success, for large datasets, training and validating a single configuration often takes hours, days, or even weeks, which limits the achievable performance. To accelerate hyperparameter optimization, we propose a generative model for the validation error as a function of training set size, which is learned during the optimization process and allows exploration of preliminary configurations on small subsets, by extrapolating to the full dataset. We construct a Bayesian optimization procedure, dubbed Fabolas, which models loss and training time as a function of dataset size and automatically trades off high information gain about the global optimum against computational cost. Experiments optimizing support vector machines and deep neural networks show that Fabolas often finds high-quality solutions 10 to 100 times faster than other state-of-the-art Bayesian optimization methods or the recently proposed bandit strategy Hyperband.
Selecting optimal parameters for a neural network architecture can often make the difference between mediocre and state-of-the-art performance. However, little is published which parameters and design choices should be evaluated or selected making the correct hyperparameter optimization often a "black art that requires expert experiences" (Snoek et al., 2012). In this paper, we evaluate the importance of different network design choices and hyperparameters for five common linguistic sequence tagging tasks (POS, Chunking, NER, Entity Recognition, and Event Detection). We evaluated over 50.000 different setups and found, that some parameters, like the pre-trained word embeddings or the last layer of the network, have a large impact on the performance, while other parameters, for example the number of LSTM layers or the number of recurrent units, are of minor importance. We give a recommendation on a configuration that performs well among different tasks.
A great variety of text tasks such as topic or spam identification, user profiling, and sentiment analysis can be posed as a supervised learning problem and tackle using a text classifier. A text classifier consists of several subprocesses, some of them are general enough to be applied to any supervised learning problem, whereas others are specifically designed to tackle a particular task, using complex and computational expensive processes such as lemmatization, syntactic analysis, etc. Contrary to traditional approaches, we propose a minimalistic and wide system able to tackle text classification tasks independent of domain and language, namely microTC. It is composed by some easy to implement text transformations, text representations, and a supervised learning algorithm. These pieces produce a competitive classifier even in the domain of informally written text. We provide a detailed description of microTC along with an extensive experimental comparison with relevant state-of-the-art methods. mircoTC was compared on 30 different datasets. Regarding accuracy, microTC obtained the best performance in 20 datasets while achieves competitive results in the remaining 10. The compared datasets include several problems like topic and polarity classification, spam detection, user profiling and authorship attribution. Furthermore, it is important to state that our approach allows the usage of the technology even without knowledge of machine learning and natural language processing.
We study two procedures (reverse-mode and forward-mode) for computing the gradient of the validation error with respect to the hyperparameters of any iterative learning algorithm such as stochastic gradient descent. These procedures mirror two methods of computing gradients for recurrent neural networks and have different trade-offs in terms of running time and space requirements. Our formulation of the reverse-mode procedure is linked to previous work by Maclaurin et al. [2015] but does not require reversible dynamics. The forward-mode procedure is suitable for real-time hyperparameter updates, which may significantly speed up hyperparameter optimization on large datasets. We present experiments on data cleaning and on learning task interactions. We also present one large-scale experiment where the use of previous gradient-based methods would be prohibitive.
We give a simple, fast algorithm for hyperparameter optimization inspired by techniques from the analysis of Boolean functions. We focus on the high-dimensional regime where the canonical example is training a neural network with a large number of hyperparameters. The algorithm --- an iterative application of compressed sensing techniques for orthogonal polynomials --- requires only uniform sampling of the hyperparameters and is thus easily parallelizable. Experiments for training deep neural networks on Cifar-10 show that compared to state-of-the-art tools (e.g., Hyperband and Spearmint), our algorithm finds significantly improved solutions, in some cases better than what is attainable by hand-tuning. In terms of overall running time (i.e., time required to sample various settings of hyperparameters plus additional computation time), we are at least an order of magnitude faster than Hyperband and Bayesian Optimization. We also outperform Random Search 8x. Additionally, our method comes with provable guarantees and yields the first improvements on the sample complexity of learning decision trees in over two decades. In particular, we obtain the first quasi-polynomial time algorithm for learning noisy decision trees with polynomial sample complexity.