# Stochastic Conjugate Gradient Algorithm with Variance Reduction

arXiv: https://arxiv.org/abs/1710.09979 · HTML: https://mlsanity.com/paper/1710.09979/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2017.

## Built on by (most cited first, 5 of 5)

- [The Stochastic Conjugate Subgradient Algorithm For Kernel Support Vector Machines](https://mlsanity.com/paper/2407.21091/) (2024)
- [Beyond First-Order: Training LLMs with Stochastic Conjugate Subgradients and AdamW](https://mlsanity.com/paper/2507.01241/) (2025)
- [Effectively Leveraging Momentum Terms in Stochastic Line Search Frameworks for Fast Optimization of Finite-Sum Problems](https://mlsanity.com/paper/2411.07102/) (2024)
- [FastAdaBelief: Improving Convergence Rate for Belief-based Adaptive Optimizers by Exploiting Strong Convexity](https://mlsanity.com/paper/2104.13790/) (2021)
- [Adaptive Learning Rate and Momentum for Training Deep Neural Networks](https://mlsanity.com/paper/2106.11548/) (2021)

## Abstract (arXiv)

Conjugate gradient (CG) methods are a class of important methods for solving linear equations and nonlinear optimization problems. In this paper, we propose a new stochastic CG algorithm with variance reduction and we prove its linear convergence with the Fletcher and Reeves method for strongly convex and smooth functions. We experimentally demonstrate that the CG with variance reduction algorithm converges faster than its counterparts for four learning models, which may be convex, nonconvex or nonsmooth. In addition, its area under the curve performance on six large-scale data sets is comparable to that of the LIBLINEAR solver for the L2-regularized L2-loss but with a significant improvement in computational efficiency