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An Inexact and Self-Adaptive ADMM Algorithm for Federated Learning


Core Concepts
The core message of this paper is to propose an inexact and self-adaptive FedADMM algorithm, termed FedADMM-InSa, to address the challenges in current FedADMM methods, including the need to empirically set the local training accuracy and the penalty parameter.
Abstract
The paper presents an inexact and self-adaptive FedADMM algorithm, FedADMM-InSa, to improve the performance of federated learning (FL) algorithms. Key highlights: An inexactness criterion is designed to enable each client to dynamically adjust the precision of local training in each communication round, without the need to empirically set the number of gradient descent steps or perceived constant accuracy. A self-adaptive scheme is developed to dynamically adjust each client's penalty parameter based on the discrepancy between its local model parameters and the global model parameters, avoiding unexpected performance deterioration due to improperly chosen fixed penalty parameters. The convergence of the proposed algorithm using the inexactness criterion is analyzed under the assumption of strongly convex loss functions. Extensive numerical experiments on both synthetic and real-world datasets demonstrate the improved performance of the proposed inexactness criterion and self-adaptive penalty adjusting scheme, reducing the clients' local computational load by 64.3% while accelerating the learning process when compared to the vanilla FedADMM.
Stats
The authors generate synthetic data for the linear regression problem by sampling from the standard normal distribution, Student's t distribution, and uniform distribution. For the image classification problem, the MNIST dataset is used, which contains 28x28 grayscale images of handwritten digits.
Quotes
"To address the above challenges, we propose an inexact and self-adaptive FedADMM algorithm, referred to as FedADMM-InSa." "Our approach eliminates the need to manually set gradient descent steps or predefine a constant accuracy. This provides each client with the flexibility to solve its subproblem inexactly based on its unique situation, thereby eliminating the potential straggler effect." "The scheme dynamically balances the primal and dual residuals defined by the dissimilarity between the client's local parameters and the server's global parameters between two communication rounds. This adaptive scheme significantly enhances the robustness of our algorithm and eliminates the risk associated with selecting inappropriate penalty parameters for individual clients."

Key Insights Distilled From

by Yongcun Song... at arxiv.org 04-12-2024

https://arxiv.org/pdf/2402.13989.pdf
FedADMM-InSa

Deeper Inquiries

How can the proposed inexactness criterion and self-adaptive penalty parameter scheme be extended to other federated learning algorithms beyond FedADMM

The proposed inexactness criterion and self-adaptive penalty parameter scheme can be extended to other federated learning algorithms by incorporating them into the optimization process of those algorithms. For instance, in federated averaging (FedAvg), the inexactness criterion can be used to guide the local updates of the clients, allowing them to adjust the precision of their updates based on their unique conditions. This can help in reducing the computational load on clients and improving the overall convergence of the algorithm. Similarly, the self-adaptive penalty parameter scheme can be applied to dynamically adjust the penalty parameters in algorithms like FedProx or FedAvg, enhancing their robustness and adaptability to heterogeneous data and computational resources.

What are the potential drawbacks or limitations of the current FedADMM-InSa algorithm, and how can they be addressed in future research

One potential drawback of the current FedADMM-InSa algorithm is the complexity introduced by the self-adaptive penalty parameter scheme. The dynamic adjustment of the penalty parameters for each client may increase the computational overhead and require additional tuning of parameters like µ and τ. To address this limitation, future research could focus on optimizing the self-adaptive scheme to make it more efficient and easier to implement. Additionally, the algorithm's convergence properties under varying penalty parameters could be further analyzed to ensure stability and convergence guarantees in all scenarios.

Can the ideas of inexactness and self-adaptation be applied to improve the performance of other distributed optimization algorithms beyond federated learning

The ideas of inexactness and self-adaptation can be applied to improve the performance of other distributed optimization algorithms beyond federated learning. For example, in decentralized optimization algorithms like decentralized gradient descent or decentralized ADMM, the inexactness criterion can be used to guide the local updates of individual nodes, reducing communication overhead and improving convergence speed. The self-adaptive penalty parameter scheme can also be beneficial in scenarios where nodes have varying computational resources or data distributions, ensuring better performance and robustness of the optimization process. By incorporating these concepts into a wide range of distributed optimization algorithms, researchers can enhance their efficiency and scalability in various applications.
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