Accelerating Federated Learning via Momentum Gradient Descent (1910.03197v2)

Abstract: Federated learning (FL) provides a communication-efficient approach to solve machine learning problems concerning distributed data, without sending raw data to a central server. However, existing works on FL only utilize first-order gradient descent (GD) and do not consider the preceding iterations to gradient update which can potentially accelerate convergence. In this paper, we consider momentum term which relates to the last iteration. The proposed momentum federated learning (MFL) uses momentum gradient descent (MGD) in the local update step of FL system. We establish global convergence properties of MFL and derive an upper bound on MFL convergence rate. Comparing the upper bounds on MFL and FL convergence rate, we provide conditions in which MFL accelerates the convergence. For different machine learning models, the convergence performance of MFL is evaluated based on experiments with MNIST dataset. Simulation results comfirm that MFL is globally convergent and further reveal significant convergence improvement over FL.

• The paper introduces MFL, which integrates a momentum term in local updates to accelerate convergence in distributed learning systems.
• The paper rigorously derives convergence bounds under strong convexity and Lipschitz conditions, outperforming traditional federated learning methods.
• The paper validates the approach on the MNIST dataset, demonstrating significant speed gains across various machine learning models.

Accelerating Federated Learning via Momentum Gradient Descent

The paper "Accelerating Federated Learning via Momentum Gradient Descent" by Wei Liu, Li Chen, Yunfei Chen, and Wenyi Zhang introduces an enhancement to traditional federated learning (FL) techniques, aimed at improving convergence rates through the integration of momentum gradient descent (MGD). The authors present a comprehensive theoretical formulation, backed by empirical validation, demonstrating the enhancement in convergence speed without compromising the communication efficiency of FL.

Federated learning is acclaimed in distributed machine learning frameworks for its ability to train models across decentralized data without centralizing raw data, thus preserving data privacy and reducing communication overhead. However, conventional FL typically employs a first-order gradient descent (GD) approach, which may converge slowly, especially under convex conditions. This research proposes a modified FL system, dubbed Momentum Federated Learning (MFL), that incorporates momentum terms during the local update phase to accelerate the convergence in iterative learning tasks.

Theoretical Contributions:

1. MFL Design: The authors leverage the insights from momentum gradient descent by introducing a momentum term in the local updates executed at the client devices in FL systems. Specifically, they tailored the update rules to include previous iterations, thereby smoothing the optimization trajectory and reducing oscillations common in purely GD approaches. The momentum term theoretically enhances convergence by accelerating the learning process towards the optimal solution.
2. Convergence Analysis: The paper provides rigorous proofs regarding the global convergence properties of MFL. The authors establish a theoretical upper bound on the convergence rate, highlighting the specific conditions under which MFL surpasses traditional FL. Notably, the efficacy of MFL is not solely dependent on the nature of convex functions as proven by deriving an accelerated convergence rate under specific assumptions such as the strong convexity and Lipschitz continuity of the local loss functions.
3. Numerical Results: Utilizing the MNIST dataset as a benchmark, the empirical evidence showcased in the paper aligns well with the theoretical predictions. The simulations reveal that MFL consistently outperforms FL in terms of convergence speed across different machine learning models, including linear regression, logistic regression, and support vector machines (SVMs). The experiments verify significant acceleration in the convergence process attributed to the introduction of the momentum term, hence confirming the hypothesis set forth by the authors.

Implications and Future Directions:

This research introduces a valuable enhancement to the federated learning paradigm through methodological innovation. The accelerated convergence imbibed by the MFL design promises more efficient training processes across distributed systems, which is pivotal in resource-constrained settings where computational power and communication capabilities are limited. Furthermore, the synergy between MGD and FL may present broader applications across non-convex optimization scenarios common in deep learning and neural networks, potentially extending the MFL approach's utility.

Future research could explore several extensions of MFL, including the examination of non-iid data distributions, robustness to heterogeneous hardware capabilities among devices, and the integration of advanced privacy-preserving techniques. Additionally, applying MFL to large-scale, complex datasets could yield insights into its scalability and adaptability to emerging challenges in federated learning environments.

In summary, this paper delivers robust theoretical and empirical analyses that underline the benefits of momentum-augmented federated learning, marking a step towards more efficient and effective distributed machine learning strategies.