# Locally Adaptive Federated Learning

arXiv: https://arxiv.org/abs/2307.06306 · HTML: https://mlsanity.com/paper/2307.06306/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 44 references that are in the map.
- First posted on arXiv 12 Jul 2023.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [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)
- [Linear Convergence in Federated Learning: Tackling Client Heterogeneity and Sparse Gradients](https://mlsanity.com/paper/2102.07053/) (2021)
- [Unified Optimal Analysis of the (Stochastic) Gradient Method](https://mlsanity.com/paper/1907.04232/) (2019)
- [Adaptive Gradient Descent without Descent](https://mlsanity.com/paper/1910.09529/) (2019)
- [Sharper Convergence Guarantees for Asynchronous SGD for Distributed and Federated Learning](https://mlsanity.com/paper/2206.08307/) (2022)
- [Perturbed Iterate Analysis for Asynchronous Stochastic Optimization](https://mlsanity.com/paper/1507.06970/) (2015)
- [SGD for Structured Nonconvex Functions: Learning Rates, Minibatching and Interpolation](https://mlsanity.com/paper/2006.10311/) (2020)
- [Communication-Efficient Adaptive Federated Learning](https://mlsanity.com/paper/2205.02719/) (2022)
- [Dynamics of SGD with Stochastic Polyak Stepsizes: Truly Adaptive Variants and Convergence to Exact Solution](https://mlsanity.com/paper/2205.04583/) (2022)
- [Local Adaptivity in Federated Learning: Convergence and Consistency](https://mlsanity.com/paper/2106.02305/) (2021)
- [Local AdaAlter: Communication-Efficient Stochastic Gradient Descent with Adaptive Learning Rates](https://mlsanity.com/paper/1911.09030/) (2019)
- [Toward Communication Efficient Adaptive Gradient Method](https://mlsanity.com/paper/2109.05109/) (2021)
- [Stochastic Mirror Descent: Convergence Analysis and Adaptive Variants via the Mirror Stochastic Polyak Stepsize](https://mlsanity.com/paper/2110.15412/) (2021)
- [Stochastic Polyak Stepsize with a Moving Target](https://mlsanity.com/paper/2106.11851/) (2021)
- [Cutting Some Slack for SGD with Adaptive Polyak Stepsizes](https://mlsanity.com/paper/2202.12328/) (2022)
- [A Stochastic Proximal Polyak Step Size](https://mlsanity.com/paper/2301.04935/) (2023)
- [Communication-Compressed Adaptive Gradient Method for Distributed Nonconvex Optimization](https://mlsanity.com/paper/2111.00705/) (2021)
- [Adaptive Federated Learning with Auto-Tuned Clients](https://mlsanity.com/paper/2306.11201/) (2023)

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

- [Communication-Efficient Adaptive Batch Size Strategies for Distributed Local Gradient Methods](https://mlsanity.com/paper/2406.13936/) (2024)
- [FedGPS: Statistical Rectification Against Data Heterogeneity in Federated Learning](https://mlsanity.com/paper/2510.20250/) (2025)
- [Taking the Road Less Scheduled with Adaptive Polyak Steps](https://mlsanity.com/paper/2511.07767/) (2025)
- [Safeguarded Stochastic Polyak Step Sizes for Non-smooth Optimization: Robust Performance Without Small (Sub)Gradients](https://mlsanity.com/paper/2512.02342/) (2025)
- [Communication Efficient Federated Learning with Linear Convergence on Heterogeneous Data](https://mlsanity.com/paper/2503.15804/) (2025)
- [Adaptive Sharpness-Aware Minimization with a Polyak-type Step size: A Theory-Grounded Scheduler](https://mlsanity.com/paper/2606.01827/) (2026)
- [Why Federated Optimization Fails to Achieve Perfect Fitting? A Theoretical Perspective on Client-Side Optima](https://mlsanity.com/paper/2511.00469/) (2025)

## Abstract (arXiv)

Federated learning is a paradigm of distributed machine learning in which multiple clients coordinate with a central server to learn a model, without sharing their own training data. Standard federated optimization methods such as Federated Averaging (FedAvg) ensure balance among the clients by using the same stepsize for local updates on all clients. However, this means that all clients need to respect the global geometry of the function which could yield slow convergence. In this work, we propose locally adaptive federated learning algorithms, that leverage the local geometric information for each client function. We show that such locally adaptive methods with uncoordinated stepsizes across all clients can be particularly efficient in interpolated (overparameterized) settings, and analyze their convergence in the presence of heterogeneous data for convex and strongly convex settings. We validate our theoretical claims by performing illustrative experiments for both i.i.d. non-i.i.d. cases. Our proposed algorithms match the optimization performance of tuned FedAvg in the convex setting, outperform FedAvg as well as state-of-the-art adaptive federated algorithms like FedAMS for non-convex experiments, and come with superior generalization performance.