Federated Learning over Wireless Networks: Convergence Analysis and Resource Allocation (1910.13067v4)

Abstract: There is an increasing interest in a fast-growing machine learning technique called Federated Learning, in which the model training is distributed over mobile user equipments (UEs), exploiting UEs' local computation and training data. Despite its advantages in data privacy-preserving, Federated Learning (FL) still has challenges in heterogeneity across UEs' data and physical resources. We first propose a FL algorithm which can handle the heterogeneous UEs' data challenge without further assumptions except strongly convex and smooth loss functions. We provide the convergence rate characterizing the trade-off between local computation rounds of UE to update its local model and global communication rounds to update the FL global model. We then employ the proposed FL algorithm in wireless networks as a resource allocation optimization problem that captures the trade-off between the FL convergence wall clock time and energy consumption of UEs with heterogeneous computing and power resources. Even though the wireless resource allocation problem of FL is non-convex, we exploit this problem's structure to decompose it into three sub-problems and analyze their closed-form solutions as well as insights to problem design. Finally, we illustrate the theoretical analysis for the new algorithm with Tensorflow experiments and extensive numerical results for the wireless resource allocation sub-problems. The experiment results not only verify the theoretical convergence but also show that our proposed algorithm outperforms the vanilla FedAvg algorithm in terms of convergence rate and testing accuracy.

Federated Learning over Wireless Networks: Convergence Analysis and Resource Allocation

The paper "Federated Learning over Wireless Networks: Convergence Analysis and Resource Allocation" addresses the growing interest in Federated Learning (FL), particularly in scenarios involving wireless networks. Federated Learning is a collaborative machine learning approach wherein model training is distributed among mobile user equipment (UEs) or devices at the edge, thereby preserving data privacy and reducing the necessity for data transmission to centralized data centers. This paper specifically explores the challenges posed by the heterogeneity of data and resources across UEs and introduces the FEDL algorithm, designed to efficiently handle these challenges without strict assumptions on data distributions.

Key Contributions and Findings

1. FEDL Algorithm: The authors propose FEDL, a novel FL algorithm that intervenes in the local UE data heterogeneity issue. Importantly, the algorithm does not rely on additional assumptions beyond the requirements of strongly convex and smooth loss functions. One of the notable aspects of FEDL is its ability to offer a linear convergence rate, which effectively quantifies the trade-off between local computation rounds (each UE updating its local model) and global communication iterations (wherein the global model is collectively updated across UEs).
2. Convergence Analysis: The paper presents a rigorous convergence analysis of FEDL, establishing its linear convergence rate under conditions of strongly convex and smooth loss functions. The analysis highlights a crucial balance between local accuracy and global learning rate, underpinning the algorithm's effectiveness compared to traditional FL algorithms like FedAvg, particularly in scenarios with heterogeneous UE data settings.
3. Resource Allocation in Wireless Networks: The paper innovatively extends FEDL to encompass resource allocation challenges in wireless networks. This is structured as an optimization problem balancing the minimization of both training time and UE energy consumption. Despite the inherent non-convexity, the problem is adeptly decomposed into three tractable sub-problems, each endowed with closed-form solutions. These solutions furnish insights into optimal UE resource allocation concerning computation, power, and communication parameters.
4. Empirical Evaluation and Numerical Results: Experimental validation using PyTorch demonstrates that FEDL exhibits superior performance metrics, including faster convergence rates and improved test accuracies, outperforming existing algorithms like FedAvg. The extensive numerical results from the sub-problems reinforce the resource allocation model's efficacy, spotlighting its practical utility in real-world wireless network scenarios.

Practical and Theoretical Implications

The advancements proposed in this paper bear significant implications:

• Practical Implementation: FEDL's ability to balance energy consumption and training time makes it highly applicable to real-world distributed learning settings involving mobile and IoT networks. The algorithm's potential to handle heterogeneous data without stringent prerequisites enhances its deployability across diverse industry domains.
• Theoretical Advances in FL: By relaxing typical assumptions on data distributions, the paper broadens the theoretical landscape for FL, particularly in edge computing environments with significant heterogeneity. The convergence guarantees and resource allocation insights are valuable contributions to ongoing developments in decentralized learning frameworks.

Future Developments

The methodology and findings pave avenues for further exploration in FL:

• Non-convex Loss Functions: Despite FEDL being demonstrated empirically in non-convex settings, a formal theoretical extension to cover non-convex loss functions could provide a more comprehensive theoretical grounding.
• Dynamic Resource Allocation: While the paper offers solutions to a static resource allocation problem, investigating dynamic scenarios could further enhance FEDL's adaptivity to fluctuating network conditions and UE capabilities.
• Broader Network Topologies: Expanding the framework to consider diverse network topologies beyond the assumed wireless setting could potentially cater to more complex and large-scale distributed environments.

This paper constitutes a substantial step forward in federated learning research, elucidating a path toward integrating machine learning models at the edge within heterogeneous and resource-constrained network environments. The introduction of FEDL, along with resource-efficient convergence guarantees, charts a course for federated systems to become the linchpin of privacy-preserving, decentralized AI innovations.