# Revisiting SGD with Increasingly Weighted Averaging: Optimization and Generalization Perspectives

arXiv: https://arxiv.org/abs/2003.04339 · HTML: https://mlsanity.com/paper/2003.04339/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 3 of 3)

- [On the Convergence of Step Decay Step-Size for Stochastic Optimization](https://mlsanity.com/paper/2102.09393/) (2021)
- [Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case](https://mlsanity.com/paper/2307.11782/) (2023)
- [Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems](https://mlsanity.com/paper/2312.01127/) (2023)

## Abstract (arXiv)

Stochastic gradient descent (SGD) has been widely studied in the literature from different angles, and is commonly employed for solving many big data machine learning problems. However, the averaging technique, which combines all iterative solutions into a single solution, is still under-explored. While some increasingly weighted averaging schemes have been considered in the literature, existing works are mostly restricted to strongly convex objective functions and the convergence of optimization error. It remains unclear how these averaging schemes affect the convergence of it both optimization error and generalization error (two equally important components of testing error) for bf non-strongly convex objectives, including non-convex problems. In this paper, we it fill the gap by comprehensively analyzing the increasingly weighted averaging on convex, strongly convex and non-convex objective functions in terms of both optimization error and generalization error. In particular, we analyze a family of increasingly weighted averaging, where the weight for the solution at iteration t is proportional to tα (α > 0). We show how α affects the optimization error and the generalization error, and exhibit the trade-off caused by α. Experiments have demonstrated this trade-off and the effectiveness of polynomially increased weighted averaging compared with other averaging schemes for a wide range of problems including deep learning.