text: ## Review Summary Overall, the paper's paper core claim, that increasing batch sizes at a linear rate during training is as effective as decaying learning rates, isinteresting  but doesn't seem to be too surprising given other recent work in this space.  The most useful part of the paper is the empirical evidence to backup this claim,  which I can't easily find in previous literature.  I wish the paper had explored a wider variety of dataset tasks and models to better show how well this claim generalizes, better situated the practical benefits of the approach  (how much wallclock time is actually saved?  how well can it be integrated into a distributed workflow?),  and included some comparisons with other recent recommended ways to increase batch size over time. ## Pros / Strengths + effort to assess momentum / Adam / other modern methods + effort to compare to previous experimental setups ## Cons / Limitations - lack of wallclock measurements in experiments - only ~2 models / datasets examined,  so difficult to assess generalization - lack of discussion about distributed/asynchronous SGD ## Significance Many recent previous efforts have looked at the importance of batch sizes during training,  so topic is relevant to the community.  Smith and Le (2017) present a differential equation model for the scale of gradients in SGD,finding a linear scaling rule proportional to eps N/B, where eps = learning rate, N = training set size, and B = batch size.  Goyal et al (2017) show how to train deep models on ImageNet effectively with large (but fixed) batch sizes by using a linear scaling rule. A few recent works have directly tested increasing batch sizes during training.  De et al (AISTATS 2017) have a method for gradually increasing batch sizes, as do Friedlander and Schmidt (2012).  Thus, it is already reasonable to practitioners that the proposed linear scaling of batch sizes during training would be effective. While increasing batch size at the proposed linear scale is simple and seems to be effective,  a careful reader will be curious how much more could be gained from the backtracking line search method proposed in De et al. ## Quality Overall, only single training runs from a random initialization are used.  It would be better to take the best of many runs or to somehow show error bars, to avoid the reader wondering whether gains are due to changes in algorithm or to poor exploration due to bad initialization.  This happens a lot in Sec. 5.2. Some of the experimental setting seem a bit haphazard and not very systematic. In Sec. 5.2, only two learning rate scales are tested (0.1 and 0.5).  Why not examine a more thorough range of values? Why not report actual wallclock times?  Of course having reduced number of parameter updates is useful,  but it's difficult to tell how big of a win this could be. What about distributed SGD or asyncronous SGD (hogwild)?  Small batch sizes sometimes make it easier for many machines to be working simultaneously.  If we scale up to batch sizes of ~ N/10, we can only get 10x speedups in parallelization (in terms of number of parameter updates).  I think there is some subtle but important discussion needed on how this framework fits into modern distributed systems for SGD. ## Clarity Overall the paper reads reasonably well. Offering a related work "feature matrix" that helps readers keep track of how previous efforts scale learning rates or minibatch sizes for specific experiments could be valueable.  Right now, lots of this information is just provided in text,  so it's not easy to make head-to-head comparisons. Several figure captions should be updated to clarify which model and dataset are studied.  For example, when skimming Fig. 3's caption there is no such information. ## Paper Summary The paper examines the influence of batch size on the behavior of stochastic gradient descent to minimize cost functions.  The central thesis is that instead of the "conventional wisdom" to fix the batch size during training and decay the learning rate, it is equally effective (in terms of training/test error reached) to gradually increase batch size during training while fixing the learning rate.  These two strategies are thus "equivalent".  Furthermore, using larger batches means fewer parameter updates per epoch,  so training is potentially much faster. Section 2 motivates the suggested linear scaling using previous SGD analysis from Smith and Le (2017).  Section 3 makes connections to previous work on finding optimal batch sizes to close the generaization gap.  Section 4 extends analysis to include SGD methods with momentum. In Section 5.1, experiments training a 16-4 ResNet on CIFAR-10 compare three possible SGD schedules:  * increasing batch size * decaying learning rate * hybrid (increasing batch size and decaying learning rate)  Fig. 2, 3 and 4 show that across a range of SGD variants (+/- momentum, etc) these three schedules have similar error vs. epoch curves.  This is the core claimed contribution: empirical evidence that these strategies are "equivalent". In Section 5.3, experiments look at Inception-ResNet-V2 on ImageNet,  showing the proposed approach can reach comparable accuracies to previous work at even fewer parameter updates (2500 here, vs. ∼14000 for Goyal et al 2007)