# Finito: A Faster, Permutable Incremental Gradient Method for Big Data Problems

arXiv: https://arxiv.org/abs/1407.2710 · HTML: https://mlsanity.com/paper/1407.2710/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2014.

## Built on by (most cited first, 10 of 10)

- [Random Reshuffling with Variance Reduction: New Analysis and Better Rates](https://mlsanity.com/paper/2104.09342/) (2021)
- [Improved Analysis and Rates for Variance Reduction under Without-replacement Sampling Orders](https://mlsanity.com/paper/2104.12112/) (2021)
- [Federated Random Reshuffling with Compression and Variance Reduction](https://mlsanity.com/paper/2205.03914/) (2022)
- [Learning with Smooth Hinge Losses](https://mlsanity.com/paper/2103.00233/) (2021)
- [A Coefficient Makes SVRG Effective](https://mlsanity.com/paper/2311.05589/) (2023)
- [Variance Reduction Methods Do Not Need to Compute Full Gradients: Improved Efficiency through Shuffling](https://mlsanity.com/paper/2502.14648/) (2025)
- [SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization](https://mlsanity.com/paper/2207.08195/) (2022)
- [Joint control variate for faster black-box variational inference](https://mlsanity.com/paper/2210.07290/) (2022)
- [Shuffling Heuristic in Variational Inequalities: Establishing New Convergence Guarantees](https://mlsanity.com/paper/2509.04133/) (2025)
- [A Short and Unified Convergence Analysis of the SAG, SAGA, and IAG Algorithms](https://mlsanity.com/paper/2602.05304/) (2026)

## Abstract (arXiv)

Recent advances in optimization theory have shown that smooth strongly convex finite sums can be minimized faster than by treating them as a black box "batch" problem. In this work we introduce a new method in this class with a theoretical convergence rate four times faster than existing methods, for sums with sufficiently many terms. This method is also amendable to a sampling without replacement scheme that in practice gives further speed-ups. We give empirical results showing state of the art performance.