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 Optimization approach. The results indicate that Differential Evolution outperforms SMAC for most datasets when tuning a given machine learning algorithm - particularly when breaking ties in a first-to-report fashion. Only for the tightest of computational budgets SMAC performs better. On small datasets, Differential Evolution outperforms SMAC by 19 (37 after tie-breaking). In a second experiment across a range of representative datasets taken from the literature, Differential Evolution scores 15 (23 after tie-breaking) more wins than SMAC.
BOHB @cite_15 is an efficient combination of Bayesian Optimization with Hyperband @cite_7 . In each BOHB iteration, a multi-armed bandit (Hyperband) determines the number of hyperparameter configurations to evaluate and the associated computational budget. This way, configurations that are likely to perform poorly are stopped early. Consequently, promising configurations receive more computing resources. The identification of configurations at the beginning of each iteration relies on Bayesian Optimization. Instead of identifying ill-performing configurations early on, our work focuses on the hyperparameter tuning aspect. In particular, we study empirically whether alternative optimization heuristics such as evolutionary algorithms can outperform the widely used model-based hyperparameter tuning approaches.
@cite_15 @cite_7
2963815651 2304209433 2598232788 2796902300
Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through adaptive resource allocation and early-stopping. We formulate hyperparameter optimization as a pure-exploration nonstochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce a novel algorithm, Hyperband, for this framework and analyze its theoretical properties, providing several desirable guarantees. Furthermore, we compare Hyperband with popular Bayesian optimization methods on a suite of hyperparameter optimization problems. We observe that Hyperband can provide over an order-of-magnitude speedup over our competitor set on a variety of deep-learning and kernel-based learning problems. Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While current methods offer efficiencies by adaptively choosing new configurations to train, an alternative strategy is to adaptively allocate resources across the selected configurations. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinitely many armed bandit problem where allocation of additional resources to an arm corresponds to training a configuration on larger subsets of the data. We introduce Hyperband for this framework and analyze its theoretical properties, providing several desirable guarantees. We compare Hyperband with state-of-the-art Bayesian optimization methods and a random search baseline on a comprehensive benchmark including 117 datasets. Our results on this benchmark demonstrate that while Bayesian optimization methods do not outperform random search trained for twice as long, Hyperband in favorable settings offers valuable speedups. The performance of many machine learning algorithms depends crucially on the hyperparameter settings, especially in Deep Learning. Manually tuning the hyperparameters is laborious and time consuming. To address this issue, Bayesian optimization (BO) methods and their extensions have been proposed to optimize the hyperparameters automatically. However, they still suffer from highly computational expense when applying to deep generative models (DGMs) due to their strategy of the black-box function optimization. This paper provides a new hyperparameter optimization procedure at the pre-training phase of the DGMs, where we avoid combining all layers as one black-box function by taking advantage of the layer-by-layer learning strategy. Following this procedure, we are able to optimize multiple hyperparameters in an adaptive way by using Gaussian process. In contrast to the traditional BO methods, which mainly focus on the supervised models, the pre-training procedure is unsupervised where there is no validation error can be used. To alleviate this problem, this paper proposes a new holdout loss, the free energy gap, which takes into account both factors of the model fitting and over-fitting. The empirical evaluations demonstrate that our method not only speeds up the process of hyperparameter optimization, but also improves the performances of DGMs significantly in both the supervised and unsupervised learning tasks. Tuning hyperparameters of machine learning models is important for their performance. Bayesian optimization has recently emerged as a de-facto method for this task. The hyperparameter tuning is usually performed by looking at model performance on a validation set. Bayesian optimization is used to find the hyperparameter set corresponding to the best model performance. However, in many cases, the function representing the model performance on the validation set contains several spurious sharp peaks due to limited datapoints. The Bayesian optimization, in such cases, has a tendency to converge to sharp peaks instead of other more stable peaks. When a model trained using these hyperparameters is deployed in the real world, its performance suffers dramatically. We address this problem through a novel stable Bayesian optimization framework. We construct two new acquisition functions that help Bayesian optimization to avoid the convergence to the sharp peaks. We conduct a theoretical analysis and guarantee that Bayesian optimization using the proposed acquisition functions prefers stable peaks over unstable ones. Experiments with synthetic function optimization and hyperparameter tuning for support vector machines show the effectiveness of our proposed framework.