# General Proximal Incremental Aggregated Gradient Algorithms: Better and Novel Results under General Scheme

arXiv: https://arxiv.org/abs/1910.05093 · HTML: https://mlsanity.com/paper/1910.05093/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2019.

## Built on by (most cited first, 6 of 6)

- [Asynchronous Iterations in Optimization: New Sequence Results and Sharper Algorithmic Guarantees](https://mlsanity.com/paper/2109.04522/) (2021)
- [Improved Analysis and Rates for Variance Reduction under Without-replacement Sampling Orders](https://mlsanity.com/paper/2104.12112/) (2021)
- [Delay-adaptive step-sizes for asynchronous learning](https://mlsanity.com/paper/2202.08550/) (2022)
- [Random-reshuffled SARAH does not need a full gradient computations](https://mlsanity.com/paper/2111.13322/) (2021)
- [Variance Reduction Methods Do Not Need to Compute Full Gradients: Improved Efficiency through Shuffling](https://mlsanity.com/paper/2502.14648/) (2025)
- [Sharpness-Aware Minimization with Adaptive Regularization for Training Deep Neural Networks](https://mlsanity.com/paper/2412.16854/) (2024)

## Abstract (arXiv)

The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence rates are also limited to linear convergence. Due to the mathematical techniques, the stepsize in the algorithm is restricted by the strongly convex constant, which may make the stepsize be very small (the strongly convex constant may be small). In this paper, we propose a general proximal incremental aggregated gradient algorithm, which contains various existing algorithms including the basic incremental aggregated gradient method. Better and new convergence results are proved even with the general scheme. The novel results presented in this paper, which have not appeared in previous literature, include: a general scheme, nonconvex analysis, the sublinear convergence rates of the function values, much larger stepsizes that guarantee the convergence, the convergence when noise exists, the line search strategy of the proximal incremental aggregated gradient algorithm and its convergence.