# CAFL-L: Constraint-Aware Federated Learning with Lagrangian Dual Optimization for On-Device Language Models

arXiv: https://arxiv.org/abs/2510.03298 · HTML: https://mlsanity.com/paper/2510.03298/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 9 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 5 of 5)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [Parameter Competition Balancing for Model Merging](https://mlsanity.com/paper/2410.02396/) (2024)

## Built on by (most cited first, 1 of 1)

- [SocioGesture: Real-Time and Adaptive Social Gesture Perception for Human-Robot Interaction](https://mlsanity.com/paper/2609.04545/) (2026)

## Abstract (arXiv)

We introduce Constraint-Aware Federated Learning with Lagrangian Dual Optimization (CAFL-L), a principled extension of FedAvg that explicitly incorporates device-level resource constraints including energy, communication, memory, and thermal budgets. CAFL-L employs Lagrangian dual optimization to dynamically adapt training hyperparameters -- freezing depth, local steps, batch size, and communication compression -- while preserving training stability through token-budget preservation via gradient accumulation. Experiments on a character-level language model demonstrate that CAFL-L achieves superior constraint satisfaction compared to standard FedAvg (reducing memory usage by 20% and communication by 95%) while maintaining competitive validation performance, making it practical for deployment on resource-constrained edge devices.