As the complexity of neural network models has grown, it has become increasingly important to optimize their design automatically through met alearning. Methods for discovering hyperparameters, topologies, and learning rate schedules have lead to significant increases in performance. This paper shows that loss functions can be optimized with met alearning as well, and result in similar improvements. The method, Genetic Loss-function Optimization (GLO), discovers loss functions de novo, and optimizes them for a target task. Leveraging techniques from genetic programming, GLO builds loss functions hierarchically from a set of operators and leaf nodes. These functions are repeatedly recombined and mutated to find an optimal structure, and then a covariance-matrix adaptation evolutionary strategy (CMA-ES) is used to find optimal coefficients. Networks trained with GLO loss functions are found to outperform the standard cross-entropy loss on standard image classification tasks. Training with these new loss functions requires fewer steps, results in lower test error, and allows for smaller datasets to be used. Loss-function optimization thus provides a new dimension of met alearning, and constitutes an important step towards AutoML.
In addition to hyperparameter optimization and neural architecture search, new opportunities for met alearning have recently emerged. In particular, learning rate scheduling and adaptation can have a significant impact on a model's performance. Learning rate schedules determine how the learning rate changes as training progresses. This functionality tends to be encapsulated away in practice by different gradient-descent optimizers, such as AdaGrad @cite_9 and Adam @cite_20 . While the general consensus has been that monotonically decreasing learning rates yield good results, new ideas, such as cyclical learning rates @cite_1 , have shown promise in learning better models in fewer epochs.
@cite_9 @cite_1 @cite_20
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It is known that the learning rate is the most important hyper-parameter to tune for training deep neural networks. This paper describes a new method for setting the learning rate, named cyclical learning rates, which practically eliminates the need to experimentally find the best values and schedule for the global learning rates. Instead of monotonically decreasing the learning rate, this method lets the learning rate cyclically vary between reasonable boundary values. Training with cyclical learning rates instead of fixed values achieves improved classification accuracy without a need to tune and often in fewer iterations. This paper also describes a simple way to estimate "reasonable bounds" -- linearly increasing the learning rate of the network for a few epochs. In addition, cyclical learning rates are demonstrated on the CIFAR-10 and CIFAR-100 datasets with ResNets, Stochastic Depth networks, and DenseNets, and the ImageNet dataset with the AlexNet and GoogLeNet architectures. These are practical tools for everyone who trains neural networks. It is known that the learning rate is the most important hyper-parameter to tune for training deep neural networks. This paper describes a new method for setting the learning rate, named cyclical learning rates, which practically eliminates the need to experimentally find the best values and schedule for the global learning rates. Instead of monotonically decreasing the learning rate, this method lets the learning rate cyclically vary between reasonable boundary values. Training with cyclical learning rates instead of fixed values achieves improved classification accuracy without a need to tune and often in fewer iterations. This paper also describes a simple way to estimate "reasonable bounds" – linearly increasing the learning rate of the network for a few epochs. In addition, cyclical learning rates are demonstrated on the CIFAR-10 and CIFAR-100 datasets with ResNets, Stochastic Depth networks, and DenseNets, and the ImageNet dataset with the AlexNet and GoogLeNet architectures. These are practical tools for everyone who trains neural networks. Despite superior training outcomes, adaptive optimization methods such as Adam, Adagrad or RMSprop have been found to generalize poorly compared to Stochastic gradient descent (SGD). These methods tend to perform well in the initial portion of training but are outperformed by SGD at later stages of training. We investigate a hybrid strategy that begins training with an adaptive method and switches to SGD when appropriate. Concretely, we propose SWATS, a simple strategy which switches from Adam to SGD when a triggering condition is satisfied. The condition we propose relates to the projection of Adam steps on the gradient subspace. By design, the monitoring process for this condition adds very little overhead and does not increase the number of hyperparameters in the optimizer. We report experiments on several standard benchmarks such as: ResNet, SENet, DenseNet and PyramidNet for the CIFAR-10 and CIFAR-100 data sets, ResNet on the tiny-ImageNet data set and language modeling with recurrent networks on the PTB and WT2 data sets. The results show that our strategy is capable of closing the generalization gap between SGD and Adam on a majority of the tasks. We describe a general framework for online adaptation of optimization hyperparameters by hot swapping' their values during learning. We investigate this approach in the context of adaptive learning rate selection using an explore-exploit strategy from the multi-armed bandit literature. Experiments on a benchmark neural network show that the hot swapping approach leads to consistently better solutions compared to well-known alternatives such as AdaDelta and stochastic gradient with exhaustive hyperparameter search.