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difficulty 3/5

Mini-batch gradient descent

Definition

Estimating the gradient from a small group of examples rather than one or all of them — the compromise that everything is actually trained with.

Formula
θt+1=θt−η 1∣B∣∑i∈B∇Li(θt)\theta_{t+1} = \theta_t - \eta \, \frac{1}{|B|}\sum_{i \in B} \nabla L_i(\theta_t)

Intuition

Full-batch gives the exact direction at a cost that grows with the dataset. Single-example SGD gives a cheap direction with a lot of noise in it. Neither extreme is what anyone runs.

Mini-batch takes 32, or 128, or 256 examples, averages their gradients, and steps. Averaging cuts the noise; the batch is still small enough that steps come quickly. Most algorithms used for deep learning "fall somewhere in between, using more than one but fewer than all the training examples" [2, §8.1.3].

Formal definition

How it works

Where it's used

Why & when

Worked example

Pitfalls

Check yourself

3 questions

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On the cheat sheet: Optimizers →

Sources

  1. Zhang, Lipton, Li, Smola. Dive into Deep Learningbook · retrieved 2026-08-31https://d2l.ai/
  2. Goodfellow, Bengio, Courville. Deep Learning (2016)book · retrieved 2026-10-06https://www.deeplearningbook.org/contents/optimization.html
  3. Goyal, Dollár, Girshick, Noordhuis, Wesolowski, Kyrola, Tulloch, Jia, He. Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour (2017)paperhttps://arxiv.org/abs/1706.02677
  4. Wu, He. Group Normalization (2018)paperhttps://arxiv.org/abs/1803.08494
  5. torch.utils.data.DataLoaderdocs · retrieved 2026-10-07https://pytorch.org/docs/stable/data.html

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