We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.
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 distributed settings for model training. The user-friendly system design simplifies creating, controlling, and tracking of a typical machine learning project. The design also allows researchers to integrate new HPO algorithms. To demonstrate its flexibility, we show how Auptimizer integrates a few major HPO techniques (from random search to neural architecture search). The code is available at https://github.com/LGE-ARC-AdvancedAI/auptimizer.
The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This requires repeated, costly, posterior inference. We provide an alternative for selecting good priors without carrying out posterior inference, building on the prior predictive distribution that marginalizes out the model parameters. We estimate virtual statistics for data generated by the prior predictive distribution and then optimize over the hyperparameters to learn ones for which these virtual statistics match target values provided by the user or estimated from (subset of) the observed data. We apply the principle for probabilistic matrix factorization, for which good solutions for prior selection have been missing. We show that for Poisson factorization models we can analytically determine the hyperparameters, including the number of factors, that best replicate the target statistics, and we study empirically the sensitivity of the approach for model mismatch. We also present a model-independent procedure that determines the hyperparameters for general models by stochastic optimization, and demonstrate this extension in context of hierarchical matrix factorization models.
Over the past half-decade, many methods have been considered for neural architecture search (NAS). Bayesian optimization (BO), which has long had success in hyperparameter optimization, has recently emerged as a very promising strategy for NAS when it is coupled with a neural predictor. Recent work has proposed different instantiations of this framework, for example, using Bayesian neural networks or graph convolutional networks as the predictive model within BO. However, the analyses in these papers often focus on the full-fledged NAS algorithm, so it is difficult to tell which individual components of the framework lead to the best performance. In this work, we give a thorough analysis of the "BO + neural predictor" framework by identifying five main components: the architecture encoding, neural predictor, uncertainty calibration method, acquisition function, and acquisition optimization strategy. We test several different methods for each component and also develop a novel path-based encoding scheme for neural architectures, which we show theoretically and empirically scales better than other encodings. Using all of our analyses, we develop a final algorithm called BANANAS, which achieves state-of-the-art performance on NAS search spaces. We adhere to the NAS research checklist (Lindauer and Hutter 2019) to facilitate best practices, and our code is available at https://github.com/naszilla/naszilla.
In many fields, a mass of algorithms with completely different hyperparameters have been developed to address the same type of problems. Choosing the algorithm and hyperparameter setting correctly can promote the overall performance greatly, but users often fail to do so due to the absence of knowledge. How to help users to effectively and quickly select the suitable algorithm and hyperparameter settings for the given task instance is an important research topic nowadays, which is known as the CASH problem. In this paper, we design the Auto-Model approach, which makes full use of known information in the related research paper and introduces hyperparameter optimization techniques, to solve the CASH problem effectively. Auto-Model tremendously reduces the cost of algorithm implementations and hyperparameter configuration space, and thus capable of dealing with the CASH problem efficiently and easily. To demonstrate the benefit of Auto-Model, we compare it with classical Auto-Weka approach. The experimental results show that our proposed approach can provide superior results and achieves better performance in a short time.
The application of deep learning to build accurate predictive models from functional neuroimaging data is often hindered by limited dataset sizes. Though data augmentation can help mitigate such training obstacles, most data augmentation methods have been developed for natural images as in computer vision tasks such as CIFAR, not for medical images. This work helps to fills in this gap by proposing a method for generating new functional Magnetic Resonance Images (fMRI) with realistic brain morphology. This method is tested on a challenging task of predicting antidepressant treatment response from pre-treatment task-based fMRI and demonstrates a 26% improvement in performance in predicting response using augmented images. This improvement compares favorably to state-of-the-art augmentation methods for natural images. Through an ablative test, augmentation is also shown to substantively improve performance when applied before hyperparameter optimization. These results suggest the optimal order of operations and support the role of data augmentation method for improving predictive performance in tasks using fMRI.
We study the problem of fitting task-specific learning rate schedules from the perspective of hyperparameter optimization, aiming at good generalization. We describe the structure of the gradient of a validation error w.r.t. the learning rate schedule -- the hypergradient. Based on this, we introduce MARTHE, a novel online algorithm guided by cheap approximations of the hypergradient that uses past information from the optimization trajectory to simulate future behaviour. It interpolates between two recent techniques, RTHO (Franceschi et al., 2017) and HD (Baydin et al. 2018), and is able to produce learning rate schedules that are more stable leading to models that generalize better.
Bayesian optimization (BO) is a model-based approach to sequentially optimize expensive black-box functions, such as the validation error of a deep neural network with respect to its hyperparameters. In many real-world scenarios, the optimization is further subject to a priori unknown constraints. For example, training a deep network configuration may fail with an out-of-memory error when the model is too large. In this work, we focus on a general formulation of Gaussian process-based BO with continuous or binary constraints. We propose constrained Max-value Entropy Search (cMES), a novel information theoretic-based acquisition function implementing this formulation. We also revisit the validity of the factorized approximation adopted for rapid computation of the MES acquisition function, showing empirically that this leads to inaccurate results. On an extensive set of real-world constrained hyperparameter optimization problems we show that cMES compares favourably to prior work, while being simpler to implement and faster than other constrained extensions of Entropy Search.
We propose probabilistic models that can extrapolate learning curves of iterative machine learning algorithms, such as stochastic gradient descent for training deep networks, based on training data with variable-length learning curves. We study instantiations of this framework based on random forests and Bayesian recurrent neural networks. Our experiments show that these models yield better predictions than state-of-the-art models from the hyperparameter optimization literature when extrapolating the performance of neural networks trained with different hyperparameter settings.
This paper studies the classification problem on electroencephalogram (EEG) data of mental tasks, using standard architecture of three-layer CNN, stacked LSTM, stacked GRU. We further propose a novel classifier - a mixed LSTM model with a CNN decoder. A hyperparameter optimization on CNN shows validation accuracy of 72% and testing accuracy of 62%. The stacked LSTM and GRU models with FFT preprocessing and downsampling on data achieve 55% and 51% testing accuracy respectively. As for the mixed LSTM model with CNN decoder, validation accuracy of 75% and testing accuracy of 70% are obtained. We believe the mixed model is more robust and accurate than both CNN and LSTM individually, by using the CNN layer as a decoder for following LSTM layers. The code is completed in the framework of Pytorch and Keras. Results and code can be found at https://github.com/theyou21/BigProject.
Working with any gradient-based machine learning algorithm involves the tedious task of tuning the optimizer's hyperparameters, such as its step size. Recent work has shown how the step size can itself be optimized alongside the model parameters by manually deriving expressions for "hypergradients" ahead of time. We show how to automatically compute hypergradients with a simple and elegant modification to backpropagation. This allows us to easily apply the method to other optimizers and hyperparameters (e.g. momentum coefficients). We can even recursively apply the method to its own hyper-hyperparameters, and so on ad infinitum. As these towers of optimizers grow taller, they become less sensitive to the initial choice of hyperparameters. We present experiments validating this for MLPs, CNNs, and RNNs. Finally, we provide a simple PyTorch implementation of this algorithm (see people.csail.mit.edu/kach/gradient-descent-the-ultimate-optimizer).
Bayesian optimization (BO) is a popular methodology to tune the hyperparameters of expensive black-box functions. Traditionally, BO focuses on a single task at a time and is not designed to leverage information from related functions, such as tuning performance objectives of the same algorithm across multiple datasets. In this work, we introduce a novel approach to achieve transfer learning across different \emph{datasets} as well as different \emph{objectives}. The main idea is to regress the mapping from hyperparameter to objective quantiles with a semi-parametric Gaussian Copula distribution, which provides robustness against different scales or outliers that can occur in different tasks. We introduce two methods to leverage this mapping: a Thompson sampling strategy as well as a Gaussian Copula process using such quantile estimate as a prior. We show that these strategies can combine the estimation of multiple objectives such as latency and accuracy, steering the hyperparameters optimization toward faster predictions for the same level of accuracy. Extensive experiments demonstrate significant improvements over state-of-the-art methods for both hyperparameter optimization and neural architecture search.
Neural architecture search methods are able to find high performance deep learning architectures with minimal effort from an expert. However, current systems focus on specific use-cases (e.g. convolutional image classifiers and recurrent language models), making them unsuitable for general use-cases that an expert might wish to write. Hyperparameter optimization systems are general-purpose but lack the constructs needed for easy application to architecture search. In this work, we propose a formal language for encoding search spaces over general computational graphs. The language constructs allow us to write modular, composable, and reusable search space encodings and to reason about search space design. We use our language to encode search spaces from the architecture search literature. The language allows us to decouple the implementations of the search space and the search algorithm, allowing us to expose search spaces to search algorithms through a consistent interface. Our experiments show the ease with which we can experiment with different combinations of search spaces and search algorithms without having to implement each combination from scratch. We release an implementation of our language with this paper.
Bayesian optimization (BO) is a successful methodology to optimize black-box functions that are expensive to evaluate. While traditional methods optimize each black-box function in isolation, there has been recent interest in speeding up BO by transferring knowledge across multiple related black-box functions. In this work, we introduce a method to automatically design the BO search space by relying on evaluations of previous black-box functions. We depart from the common practice of defining a set of arbitrary search ranges a priori by considering search space geometries that are learned from historical data. This simple, yet effective strategy can be used to endow many existing BO methods with transfer learning properties. Despite its simplicity, we show that our approach considerably boosts BO by reducing the size of the search space, thus accelerating the optimization of a variety of black-box optimization problems. In particular, the proposed approach combined with random search results in a parameter-free, easy-to-implement, robust hyperparameter optimization strategy. We hope it will constitute a natural baseline for further research attempting to warm-start BO.
We propose a new scalable method to optimize the architecture of an artificial neural network. The proposed algorithm, called Greedy Search for Neural Network Architecture, aims to determine a neural network with minimal number of layers that is at least as performant as neural networks of the same structure identified by other hyperparameter search algorithms in terms of accuracy and computational cost. Numerical results performed on benchmark datasets show that, for these datasets, our method outperforms state-of-the-art hyperparameter optimization algorithms in terms of attainable predictive performance by the selected neural network architecture, and time-to-solution for the hyperparameter optimization to complete.
Automated machine learning aims to automate the whole process of machine learning, including model configuration. In this paper, we focus on automated hyperparameter optimization (HPO) based on sequential model-based optimization (SMBO). Though conventional SMBO algorithms work well when abundant HPO trials are available, they are far from satisfactory in practical applications where a trial on a huge dataset may be so costly that an optimal hyperparameter configuration is expected to return in as few trials as possible. Observing that human experts draw on their expertise in a machine learning model by trying configurations that once performed well on other datasets, we are inspired to speed up HPO by transferring knowledge from historical HPO trials on other datasets. We propose an end-to-end and efficient HPO algorithm named as Transfer Neural Processes (TNP), which achieves transfer learning by incorporating trials on other datasets, initializing the model with well-generalized parameters, and learning an initial set of hyperparameters to evaluate. Experiments on extensive OpenML datasets and three computer vision datasets show that the proposed model can achieve state-of-the-art performance in at least one order of magnitude less trials.
Hyperparameter optimization is both a practical issue and an interesting theoretical problem in training of deep architectures. Despite many recent advances the most commonly used methods almost universally involve training multiple and decoupled copies of the model, in effect sampling the hyperparameter space. We show that at a negligible additional computational cost, results can be improved by sampling nonlocal paths instead of points in hyperparameter space. To this end we interpret hyperparameters as controlling the level of correlated noise in training, which can be mapped to an effective temperature. The usually independent instances of the model are coupled and allowed to exchange their hyperparameters throughout the training using the well established parallel tempering technique of statistical physics. Each simulation corresponds then to a unique path, or history, in the joint hyperparameter/model-parameter space. We provide empirical tests of our method, in particular for dropout and learning rate optimization. We observed faster training and improved resistance to overfitting and showed a systematic decrease in the absolute validation error, improving over benchmark results.
Recurrent neural networks are good at solving prediction problems. However, finding a network that suits a problem is quite hard because their performance is strongly affected by their architecture configuration. Automatic architecture optimization methods help to find the most suitable design, but they are not extensively adopted because of their high computational cost. In this work, we introduce the Random Error Sampling-based Neuroevolution (RESN), an evolutionary algorithm that uses the mean absolute error random sampling, a training-free approach to predict the expected performance of an artificial neural network, to optimize the architecture of a network. We empirically validate our proposal on three prediction problems, and compare our technique to training-based architecture optimization techniques and to neuroevolutionary approaches. Our findings show that we can achieve state-of-the-art error performance and that we reduce by half the time needed to perform the optimization.
Continuing advances in neural interfaces have enabled simultaneous monitoring of spiking activity from hundreds to thousands of neurons. To interpret these large-scale data, several methods have been proposed to infer latent dynamic structure from high-dimensional datasets. One recent line of work uses recurrent neural networks in a sequential autoencoder (SAE) framework to uncover dynamics. SAEs are an appealing option for modeling nonlinear dynamical systems, and enable a precise link between neural activity and behavior on a single-trial basis. However, the very large parameter count and complexity of SAEs relative to other models has caused concern that SAEs may only perform well on very large training sets. We hypothesized that with a method to systematically optimize hyperparameters (HPs), SAEs might perform well even in cases of limited training data. Such a breakthrough would greatly extend their applicability. However, we find that SAEs applied to spiking neural data are prone to a particular form of overfitting that cannot be detected using standard validation metrics, which prevents standard HP searches. We develop and test two potential solutions: an alternate validation method ("sample validation") and a novel regularization method ("coordinated dropout"). These innovations prevent overfitting quite effectively, and allow us to test whether SAEs can achieve good performance on limited data through large-scale HP optimization. When applied to data from motor cortex recorded while monkeys made reaches in various directions, large-scale HP optimization allowed SAEs to better maintain performance for small dataset sizes. Our results should greatly extend the applicability of SAEs in extracting latent dynamics from sparse, multidimensional data, such as neural population spiking activity.
Hyperparameter optimization and neural architecture search can become prohibitively expensive for regular black-box Bayesian optimization because the training and evaluation of a single model can easily take several hours. To overcome this, we introduce a comprehensive tool suite for effective multi-fidelity Bayesian optimization and the analysis of its runs. The suite, written in Python, provides a simple way to specify complex design spaces, a robust and efficient combination of Bayesian optimization and HyperBand, and a comprehensive analysis of the optimization process and its outcomes.