  Deep learning networks are typically trained by Stochastic Gradient Descent
(SGD) methods that iteratively improve the model parameters by estimating a
gradient on a very small fraction of the training data. A major roadblock faced
when increasing the batch size to a substantial fraction of the training data
for improving training time is the persistent degradation in performance
(generalization gap). To address this issue, recent work propose to add small
perturbations to the model parameters when computing the stochastic gradients
and report improved generalization performance due to smoothing effects.
However, this approach is poorly understood; it requires often model-specific
noise and fine-tuning. To alleviate these drawbacks, we propose to use instead
computationally efficient extrapolation (extragradient) to stabilize the
optimization trajectory while still benefiting from smoothing to avoid sharp
minima. This principled approach is well grounded from an optimization
perspective and we show that a host of variations can be covered in a unified
framework that we propose. We prove the convergence of this novel scheme and
rigorously evaluate its empirical performance on ResNet, LSTM, and Transformer.
We demonstrate that in a variety of experiments the scheme allows scaling to
much larger batch sizes than before whilst reaching or surpassing SOTA
accuracy.
