# Almost Tune-Free Variance Reduction

arXiv: https://arxiv.org/abs/1908.09345 · HTML: https://mlsanity.com/paper/1908.09345/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2019.

## Built on by (most cited first, 7 of 7)

- [Enhancing Sharpness-Aware Optimization Through Variance Suppression](https://mlsanity.com/paper/2309.15639/) (2023)
- [AI-SARAH: Adaptive and Implicit Stochastic Recursive Gradient Methods](https://mlsanity.com/paper/2102.09700/) (2021)
- [Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization](https://mlsanity.com/paper/2211.01851/) (2022)
- [SVRG Meets AdaGrad: Painless Variance Reduction](https://mlsanity.com/paper/2102.09645/) (2021)
- [Adaptive Accelerated (Extra-)Gradient Methods with Variance Reduction](https://mlsanity.com/paper/2201.12302/) (2022)
- [VASSO: Variance Suppression for Sharpness-Aware Minimization](https://mlsanity.com/paper/2509.02433/) (2025)
- [An Adaptive Incremental Gradient Method With Support for Non-Euclidean Norms](https://mlsanity.com/paper/2205.02273/) (2022)

## Abstract (arXiv)

The variance reduction class of algorithms including the representative ones, SVRG and SARAH, have well documented merits for empirical risk minimization problems. However, they require grid search to tune parameters (step size and the number of iterations per inner loop) for optimal performance. This work introduces `almost tune-free' SVRG and SARAH schemes equipped with i) Barzilai-Borwein (BB) step sizes; ii) averaging; and, iii) the inner loop length adjusted to the BB step sizes. In particular, SVRG, SARAH, and their BB variants are first reexamined through an `estimate sequence' lens to enable new averaging methods that tighten their convergence rates theoretically, and improve their performance empirically when the step size or the inner loop length is chosen large. Then a simple yet effective means to adjust the number of iterations per inner loop is developed to enhance the merits of the proposed averaging schemes and BB step sizes. Numerical tests corroborate the proposed methods.