# Stochastic Gradient Descent with Preconditioned Polyak Step-size

arXiv: https://arxiv.org/abs/2310.02093 · HTML: https://mlsanity.com/paper/2310.02093/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [AdaGrad stepsizes: Sharp convergence over nonconvex landscapes](https://mlsanity.com/paper/1806.01811/) (2018)
- [On the Convergence of Stochastic Gradient Descent with Adaptive Stepsizes](https://mlsanity.com/paper/1805.08114/) (2018)
- [Stochastic Polyak Step-size for SGD: An Adaptive Learning Rate for Fast Convergence](https://mlsanity.com/paper/2002.10542/) (2020)
- [Training Neural Networks for and by Interpolation](https://mlsanity.com/paper/1906.05661/) (2019)
- [Dynamics of SGD with Stochastic Polyak Stepsizes: Truly Adaptive Variants and Convergence to Exact Solution](https://mlsanity.com/paper/2205.04583/) (2022)
- [MoMo: Momentum Models for Adaptive Learning Rates](https://mlsanity.com/paper/2305.07583/) (2023)
- [Adaptive SGD with Polyak stepsize and Line-search: Robust Convergence and Variance Reduction](https://mlsanity.com/paper/2308.06058/) (2023)
- [Cutting Some Slack for SGD with Adaptive Polyak Stepsizes](https://mlsanity.com/paper/2202.12328/) (2022)
- [Doubly Adaptive Scaled Algorithm for Machine Learning Using Second-Order Information](https://mlsanity.com/paper/2109.05198/) (2021)
- [AI-SARAH: Adaptive and Implicit Stochastic Recursive Gradient Methods](https://mlsanity.com/paper/2102.09700/) (2021)
- [A Stochastic Proximal Polyak Step Size](https://mlsanity.com/paper/2301.04935/) (2023)
- [SP2: A Second Order Stochastic Polyak Method](https://mlsanity.com/paper/2207.08171/) (2022)
- [Function Value Learning: Adaptive Learning Rates Based on the Polyak Stepsize and Function Splitting in ERM](https://mlsanity.com/paper/2307.14528/) (2023)
- [Stochastic Gradient Methods with Preconditioned Updates](https://mlsanity.com/paper/2206.00285/) (2022)

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

- [Remove that Square Root: A New Efficient Scale-Invariant Version of AdaGrad](https://mlsanity.com/paper/2403.02648/) (2024)
- [New Perspectives on the Polyak Stepsize: Surrogate Functions and Negative Results](https://mlsanity.com/paper/2505.20219/) (2025)
- [SANIA: Polyak-type Optimization Framework Leads to Scale Invariant Stochastic Algorithms](https://mlsanity.com/paper/2312.17369/) (2023)
- [AdaBatchGrad: Combining Adaptive Batch Size and Adaptive Step Size](https://mlsanity.com/paper/2402.05264/) (2024)
- [Safeguarded Stochastic Polyak Step Sizes for Non-smooth Optimization: Robust Performance Without Small (Sub)Gradients](https://mlsanity.com/paper/2512.02342/) (2025)
- [Byzantine-Robust Optimization under (L0, L1)-Smoothness](https://mlsanity.com/paper/2603.12512/) (2026)
- [Why Clipping Matters in AdaGrad? Toward a High-Probability Theory under Generalized Smoothness](https://mlsanity.com/paper/2609.30276/) (2026)

## Abstract (arXiv)

Stochastic Gradient Descent (SGD) is one of the many iterative optimization methods that are widely used in solving machine learning problems. These methods display valuable properties and attract researchers and industrial machine learning engineers with their simplicity. However, one of the weaknesses of this type of methods is the necessity to tune learning rate (step-size) for every loss function and dataset combination to solve an optimization problem and get an efficient performance in a given time budget. Stochastic Gradient Descent with Polyak Step-size (SPS) is a method that offers an update rule that alleviates the need of fine-tuning the learning rate of an optimizer. In this paper, we propose an extension of SPS that employs preconditioning techniques, such as Hutchinson's method, Adam, and AdaGrad, to improve its performance on badly scaled and/or ill-conditioned datasets.