Function-Space ADMM for Decentralized Federated Learning: A Control Theoretic Perspective

Federated learning (FL) is a decentralized approach that enables collaborative model training without exposing raw data. Instead of transferring sensitive data, it allows devices to share only model weights, keeping personal data locally and secure. However, in real world settings, the data held by devices is often not evenly distributed and devices mostly differ in computing power and memory capacity. These differences make FL harder to maintain consistent performance across the system. To address these issues, we propose FedMTFI, a novel architecture that combines multi-teacher knowledge distillation (MTKD) with feature importance to improve the FL process in heterogeneous environments. In FedMTFI, clients are clustered based on similar hardware and model types. Each cluster trains a specific model on not independently and identically distributed (non-IID) data. Within a cluster, every client updates that model using only its own local private data. The server then aggregates the locally trained models in each cluster using FedAvg to form multiple prototype models. Then these prototypes serve as teacher models to train a global generalized student model using MTKD. What makes FedMTFI more unique is the integration of Shapley values (SHAP) to emphasize important features during distillation, which enhances both accuracy and interpretability. Experimental results show that FedMTFI achieves higher accuracy than traditional FL algorithms and performs more effectively under non-IID data conditions.

Decentralized intelligence systems with heterogeneous devices and limited coordination increasingly rely on decentralized federated learning (DFL). However, DFL suffers from convergence inefficiency under data heterogeneity due to the use of a uniform learning rate (LR) that ignores layer-specific optimization needs. Foundational layers are responsible for maintaining network consensus, while specialized layers adapt to local data characteristics, leading to conflicting gradients and degraded performance under non-IID conditions. To address this fundamental tension, this work introduces FedA2L, a method that dynamically adjusts layer-wise LRs based on model divergence signals. By leveraging local update intensity and network consensus constraints, FedA2L seamlessly integrates into existing DFL protocols without additional communication or coordination. Extensive evaluations across DFL algorithms, various model architectures, and datasets demonstrate that FedA2L achieves up to 4.94 times faster convergence than vanilla DFL and reduces communication rounds by up to 59% compared to scheduler-based baselines. Furthermore, FedA2L exhibits resilience to severe data heterogeneity, larger network sizes, and sparse topologies, reducing communication overhead and establishing it as a versatile optimization tool for resource-constrained or large-scale distributed learning in edge and IoT deployments. The code is released at https://github.com/nclabteam/FedA2L.

Federated Learning (FL) enables collaborative model training without centralizing data. However, real-world deployments must simultaneously address statistical heterogeneity across client data (non-IID), system heterogeneity in device capabilities, and communication efficiency. Existing FL approaches mitigate these challenges through improved aggregation, personalization, or knowledge distillation, but they almost universally assume a fixed client architecture, limiting adaptability to heterogeneous data complexity and hardware constraints. This architectural constraint often leads to suboptimal trade-offs between accuracy and efficiency in real-world FL systems. This work introduces FedKDNAS, a distillation-driven FL framework that combines client-side neural architecture selection with distillation of server-coordinated knowledge. Each client autonomously selects a lightweight model under accuracy-resource constraints. It then trains it locally using a hybrid objective combining supervised learning and knowledge distillation and shares only predictions on a public reference set. The server then aggregates and smooths these predictions, optionally combining them with a teacher model, to produce stable distillation targets for the next round. Extensive evaluation on six datasets against six representative FL baselines (FedAvg, Ditto, FedMD, FedDF, FedDistill, Local-KD) demonstrates that FedKDNAS consistently achieves superior Pareto efficiency, improving accuracy by up to 15% under non-IID conditions, reducing client CPU usage by approximately 28%, and decreasing communication overhead by up to 44 times while maintaining lightweight logit-based communication.