Hyperparameter Tuning and Implicit Regularization in Minibatch SGD
This paper makes two contributions towards understanding how the hyperparameters of stochastic gradient descent affect the final training loss and test accuracy of neural networks. First, we argue that stochastic gradient descent exhibits two regimes with different behaviours; a noise dominated regime which typically arises for small or moderate batch sizes, and a curvature dominated regime which typically arises when the batch size is large. In the noise dominated regime, the optimal learning rate increases as the batch size rises, and the training loss and test accuracy are independent of batch size under a constant epoch budget. In the curvature dominated regime, the optimal learning rate is independent of batch size, and the training loss and test accuracy degrade as the batch size rises. We support these claims with experiments on a range of architectures including ResNets, LSTMs and autoencoders. We always perform a grid search over learning rates at all batch sizes. Second, we demonstrate that small or moderately large batch sizes continue to outperform very large batches on the test set, even when both models are trained for the same number of steps and reach similar training losses. Furthermore, when training Wide-ResNets on CIFAR-10 with a constant batch size of 64, the optimal learning rate to maximize the test accuracy only decays by a factor of 2 when the epoch budget is increased by a factor of 128, while the optimal learning rate to minimize the training loss decays by a factor of 16. These results confirm that the noise in stochastic gradients can introduce beneficial implicit regularization.
This paper is an empirical contribution regarding SGD arguing that it presents two different behaviors which the authors name a noise dominated regimen, and a curvature dominated regime. They observe that the behaviors seem to arise in different batch sizes The authors derive empirical conclusions and perform experiments in different settings. The paper is well-written and the experimental setup seems to be carefully carried out. I find the observations interesting, but the contribution is empirical and not entirely new. It would be nice if there were some theoretical results to back up the observations.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Hyperparameter Tuning and Implicit Regularization in Minibatch SGD
This paper makes two contributions towards understanding how the hyperparameters of stochastic gradient descent affect the final training loss and test accuracy of neural networks. First, we argue that stochastic gradient descent exhibits two regimes with different behaviours; a noise dominated regime which typically arises for small or moderate batch sizes, and a curvature dominated regime which typically arises when the batch size is large. In the noise dominated regime, the optimal learning rate increases as the batch size rises, and the training loss and test accuracy are independent of batch size under a constant epoch budget. In the curvature dominated regime, the optimal learning rate is independent of batch size, and the training loss and test accuracy degrade as the batch size rises. We support these claims with experiments on a range of architectures including ResNets, LSTMs and autoencoders. We always perform a grid search over learning rates at all batch sizes. Second, we demonstrate that small or moderately large batch sizes continue to outperform very large batches on the test set, even when both models are trained for the same number of steps and reach similar training losses. Furthermore, when training Wide-ResNets on CIFAR-10 with a constant batch size of 64, the optimal learning rate to maximize the test accuracy only decays by a factor of 2 when the epoch budget is increased by a factor of 128, while the optimal learning rate to minimize the training loss decays by a factor of 16. These results confirm that the noise in stochastic gradients can introduce beneficial implicit regularization.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



This paper is an empirical contribution regarding SGD arguing that it presents two different behaviors which the authors name a noise dominated regimen, and a curvature dominated regime. They observe that the behaviors seem to arise in different batch sizes The authors derive empirical conclusions and perform experiments in different settings. The paper is well-written and the experimental setup seems to be carefully carried out. I find the observations interesting, but the contribution is empirical and not entirely new. It would be nice if there were some theoretical results to back up the observations.
assistant
This paper is an empirical contribution regarding SGD arguing that it presents two different behaviors which the authors name a noise dominated regimen, and a curvature dominated regime. They observe that the behaviors seem to arise in different batch sizes The authors derive empirical conclusions and perform experiments in different settings. The paper is well-written and the experimental setup seems to be carefully carried out. I find the observations interesting, but the contribution is empirical and not entirely new. It would be nice if there were some theoretical results to back up the observations.