# Adaptive Federated Learning via Dynamical System Model

arXiv: https://arxiv.org/abs/2510.04203 · HTML: https://mlsanity.com/paper/2510.04203/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 27 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 22 of 22)

- [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)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [An Exponential Learning Rate Schedule for Deep Learning](https://mlsanity.com/paper/1910.07454/) (2019)
- [FedSplit: An algorithmic framework for fast federated optimization](https://mlsanity.com/paper/2005.05238/) (2020)
- [FedDANE: A Federated Newton-Type Method](https://mlsanity.com/paper/2001.01920/) (2020)
- [FedExP: Speeding Up Federated Averaging via Extrapolation](https://mlsanity.com/paper/2301.09604/) (2023)
- [Understanding Optimization in Deep Learning with Central Flows](https://mlsanity.com/paper/2410.24206/) (2024)
- [Faster Non-Convex Federated Learning via Global and Local Momentum](https://mlsanity.com/paper/2012.04061/) (2020)
- [STEM: A Stochastic Two-Sided Momentum Algorithm Achieving Near-Optimal Sample and Communication Complexities for Federated Learning](https://mlsanity.com/paper/2106.10435/) (2021)
- [On the Outsized Importance of Learning Rates in Local Update Methods](https://mlsanity.com/paper/2007.00878/) (2020)
- [Faster Adaptive Federated Learning](https://mlsanity.com/paper/2212.00974/) (2022)
- [Server-Side Stepsizes and Sampling Without Replacement Provably Help in Federated Optimization](https://mlsanity.com/paper/2201.11066/) (2022)
- [FedFisher: Leveraging Fisher Information for One-Shot Federated Learning](https://mlsanity.com/paper/2403.12329/) (2024)
- [Coordinating Momenta for Cross-silo Federated Learning](https://mlsanity.com/paper/2102.03970/) (2021)
- [Adaptive Federated Learning with Auto-Tuned Clients](https://mlsanity.com/paper/2306.11201/) (2023)
- [FedCAda: Adaptive Client-Side Optimization for Accelerated and Stable Federated Learning](https://mlsanity.com/paper/2405.11811/) (2024)
- [An Equivalent Circuit Approach to Distributed Optimization](https://mlsanity.com/paper/2305.14607/) (2023)
- [FedECADO: A Dynamical System Model of Federated Learning](https://mlsanity.com/paper/2410.09933/) (2024)

## Abstract (arXiv)

Hyperparameter selection is critical for stable and efficient convergence of heterogeneous federated learning, where clients differ in computational capabilities, and data distributions are non-IID. Tuning hyperparameters is a manual and computationally expensive process as the hyperparameter space grows combinatorially with the number of clients. To address this, we introduce an end-to-end adaptive federated learning method in which both clients and central agents adaptively select their local learning rates and momentum parameters. Our approach models federated learning as a dynamical system, allowing us to draw on principles from numerical simulation and physical design. Through this perspective, selecting momentum parameters equates to critically damping the system for fast, stable convergence, while learning rates for clients and central servers are adaptively selected to satisfy accuracy properties from numerical simulation. The result is an adaptive, momentum-based federated learning algorithm in which the learning rates for clients and servers are dynamically adjusted and controlled by a single, global hyperparameter. By designing a fully integrated solution for both adaptive client updates and central agent aggregation, our method is capable of handling key challenges of heterogeneous federated learning, including objective inconsistency and client drift. Importantly, our approach achieves fast convergence while being insensitive to the choice of the global hyperparameter, making it well-suited for rapid prototyping and scalable deployment. Compared to state-of-the-art adaptive methods, our framework is shown to deliver superior convergence for heterogeneous federated learning while eliminating the need for hyperparameter tuning both client and server updates.