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Using Machine Learning to Discover Neural Network Optimizers
Wednesday, March 28, 2018
Posted by Irwan Bello, Research Associate, Google Brain Team
Deep learning
models have been deployed in numerous Google products, such as
Search
,
Translate
and
Photos
. The choice of optimization method plays a major role when training deep learning models. For example,
stochastic gradient descent
works well in many situations, but
more advanced optimizers
can be faster, especially for training very deep networks. Coming up with new optimizers for neural networks, however, is challenging due to to the
non-convex
nature of the optimization problem. On the
Google Brain team
, we wanted to see if it could be possible to automate the discovery of new optimizers, in a way that is similar to how
AutoML
has been used to discover new competitive neural network architectures.
In “
Neural Optimizer Search with Reinforcement Learning
”, we present a method to discover optimization methods with a focus on deep learning architectures. Using this method we found two new optimizers,
PowerSign
and
AddSign
, that are competitive on a variety of different tasks and architectures, including
ImageNet
classification and Google’s neural machine translation system. To help others benefit from this work we have made the optimizers available in
Tensorflow
.
Neural Optimizer Search makes use of a
recurrent neural network
controller which is given access to a list of simple primitives that are typically relevant for optimization. These primitives include, for example, the gradient or the running average of the gradient and lead to search spaces with over 10
10
possible combinations. The controller then generates the computation graph for a candidate optimizer or update rule in that search space.
In our paper, proposed candidate update rules (U) are used to train a child
convolutional neural network
on
CIFAR10
for a few epochs and the final validation accuracy (R) is fed as a reward to the controller. The controller is trained with
reinforcement learning
to maximize the validation accuracies of the sampled update rules. This process is illustrated below.
An overview of Neural Optimizer Search using an iterative process to discover new optimizers.
Interestingly, the optimizers we have found are interpretable. For example, in the
PowerSign
optimizer we are releasing, each update compares the sign of the gradient and its running average, adjusting the step size according to whether those two values agree. The intuition behind this is that if these values agree, one is more confident in the direction of the update, and thus the step size can be larger. We also discovered a simple learning rate decay scheme,
linear cosine decay
, which we found can lead to faster convergence.
Graph comparing learning rate decay functions for
linear cosine decay
, stepwise decay and
cosine decay
.
Neural Optimizer Search found several optimizers that outperform commonly used optimizers on the small
ConvNet
model. Among the ones that transfer well to other tasks, we found that
PowerSign
and
AddSign
improve top-1 and top-5 accuracy of a state-of-the-art ImageNet mobile-sized model by up to 0.4%. They also work well on Google’s
Neural Machine Translation
system, giving an improvement of up to 0.7 using bilingual evaluation metrics (
BLEU
) on an English to German translation task.
We are excited that
Neural Optimizer Search
can not only improve the performance of machine learning models but also potentially lead to new, interpretable equations and discoveries. It is our hope that
open sourcing these optimizers in Tensorflow
will be useful to machine learning practitioners.
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