A State Alignment-Centric Approach to Federated System Identification: The FedAlign Framework

2025-03-15

AI Summary

This paper addresses the distortion in FedAvg aggregation for system identification tasks in federated learning (FL), arising from local dynamic heterogeneity in state-space models (SSMs). To resolve this, we propose FedAlign—a framework that aligns local SSM state representations via similarity transformations to establish a unified parameter space. We introduce the novel “state-aligned centralization” paradigm and design two complementary alignment mechanisms: an analytical approach (FedAlign-A) and an optimization-based approach (FedAlign-O), effectively tackling the non-uniqueness of controllable canonical forms in multi-input multi-output settings. The method integrates control-theoretic concepts—including controllable canonical forms and similarity transformations—with federated learning and least-squares optimization. Extensive experiments on synthetic and real-world datasets demonstrate that FedAlign significantly outperforms FedAvg: it achieves faster convergence and yields global models with higher dynamical fidelity and improved stability.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Intelligent Robots: State Estimation
• Multiagent Systems: Adversarial Agents

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper presents FedAlign, a Federated Learning (FL) framework particularly designed for System Identification (SYSID) tasks by aligning state representations. Local workers can learn State-Space Models (SSMs) with equivalent representations but different dynamics. We demonstrate that directly aggregating these local SSMs via FedAvg results in a global model with altered system dynamics. FedAlign overcomes this problem by employing similarity transformation matrices to align state representations of local SSMs, thereby establishing a common parameter basin that retains the dynamics of local SSMs. FedAlign computes similarity transformation matrices via two distinct approaches: FedAlign-A and FedAlign-O. In FedAlign-A, we represent the global SSM in controllable canonical form (CCF). We apply control theory to analytically derive similarity transformation matrices that convert each local SSM into this form. Yet, establishing global SSM in CCF brings additional alignment challenges in multi input - multi output SYSID as CCF representation is not unique, unlike in single input - single output SYSID. In FedAlign-O, we address these alignment challenges by reformulating the local parameter basin alignment problem as an optimization task. We determine the parameter basin of a local worker as the common parameter basin and solve least square problems to obtain similarity transformation matrices needed to align the remaining local SSMs. Through the experiments conducted on synthetic and real-world datasets, we show that FedAlign outperforms FedAvg, converges faster, and provides improved stability of the global SSM thanks to the efficient alignment of local parameter basins.

Problem

• Aligns state representations in federated system identification tasks.
• Overcomes altered dynamics in global models via similarity transformations.
• Improves stability and convergence in federated learning for system identification.

Innovation

• FedAlign aligns state representations in federated learning.
• Uses similarity transformation matrices for model alignment.
• Offers FedAlign-A and FedAlign-O for different alignment strategies.