# Why Does Multi-Epoch Training Help?

arXiv: https://arxiv.org/abs/2105.06015 · HTML: https://mlsanity.com/paper/2105.06015/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 39 references that are in the map.
- First posted on arXiv 13 May 2021.

## Builds on (most cited first, 24 of 24)

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Bag of Tricks for Image Classification with Convolutional Neural Networks](https://mlsanity.com/paper/1812.01187/) (2018)
- [Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks](https://mlsanity.com/paper/1811.08888/) (2018)
- [Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08157/) (2020)
- [Stability and Generalization of Learning Algorithms that Converge to Global Optima](https://mlsanity.com/paper/1710.08402/) (2017)
- [High probability generalization bounds for uniformly stable algorithms with nearly optimal rate](https://mlsanity.com/paper/1902.10710/) (2019)
- [Data-Dependent Stability of Stochastic Gradient Descent](https://mlsanity.com/paper/1703.01678/) (2017)
- [Small ReLU networks are powerful memorizers: a tight analysis of memorization capacity](https://mlsanity.com/paper/1810.07770/) (2018)
- [Statistical Optimality of Stochastic Gradient Descent on Hard Learning Problems through Multiple Passes](https://mlsanity.com/paper/1805.10074/) (2018)
- [A Simple Proximal Stochastic Gradient Method for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/1802.04477/) (2018)
- [Generalization Properties and Implicit Regularization for Multiple Passes SGM](https://mlsanity.com/paper/1605.08375/) (2016)
- [Empirical Risk Minimization for Stochastic Convex Optimization: O(1/n)- and O(1/n2)-type of Risk Bounds](https://mlsanity.com/paper/1702.02030/) (2017)
- [Generalization Error Bounds with Probabilistic Guarantee for SGD in Nonconvex Optimization](https://mlsanity.com/paper/1802.06903/) (2018)
- [Fast Rates of ERM and Stochastic Approximation: Adaptive to Error Bound Conditions](https://mlsanity.com/paper/1805.04577/) (2018)

## Built on by (most cited first, 1 of 1)

- [Less Data, Faster Training: repeating smaller datasets speeds up learning via sampling biases](https://mlsanity.com/paper/2605.20314/) (2026)

## Abstract (arXiv)

Stochastic gradient descent (SGD) has become the most attractive optimization method in training large-scale deep neural networks due to its simplicity, low computational cost in each updating step, and good performance. Standard excess risk bounds show that SGD only needs to take one pass over the training data and more passes could not help to improve the performance. Empirically, it has been observed that SGD taking more than one pass over the training data (multi-pass SGD) has much better excess risk bound performance than the SGD only taking one pass over the training data (one-pass SGD). However, it is not very clear that how to explain this phenomenon in theory. In this paper, we provide some theoretical evidences for explaining why multiple passes over the training data can help improve performance under certain circumstance. Specifically, we consider smooth risk minimization problems whose objective function is non-convex least squared loss. Under Polyak-Lojasiewicz (PL) condition, we establish faster convergence rate of excess risk bound for multi-pass SGD than that for one-pass SGD.