Federated Learning with Matched Averaging (2002.06440v1)

Abstract: Federated learning allows edge devices to collaboratively learn a shared model while keeping the training data on device, decoupling the ability to do model training from the need to store the data in the cloud. We propose Federated matched averaging (FedMA) algorithm designed for federated learning of modern neural network architectures e.g. convolutional neural networks (CNNs) and LSTMs. FedMA constructs the shared global model in a layer-wise manner by matching and averaging hidden elements (i.e. channels for convolution layers; hidden states for LSTM; neurons for fully connected layers) with similar feature extraction signatures. Our experiments indicate that FedMA not only outperforms popular state-of-the-art federated learning algorithms on deep CNN and LSTM architectures trained on real world datasets, but also reduces the overall communication burden.

• The paper introduces FedMA, which aligns neurons across clients to handle permutation invariance in neural networks.
• It employs layer-wise matching using the Hungarian algorithm to reduce communication rounds while enhancing convergence speed.
• FedMA maintains stable performance with extended local training and effectively mitigates data biases across diverse model architectures.

Federated Learning with Matched Averaging

Federated learning has emerged as a pivotal paradigm to address the burgeoning data privacy concerns and network bandwidth limitations associated with centralized data training. The paper "Federated Learning with Matched Averaging," authored by Hongyi Wang et al., introduces the Federated Matched Averaging (FedMA) algorithm, designed to optimize federated learning for modern neural network architectures such as CNNs and LSTMs.

Overview

FedMA is premised on the federated learning framework, where edge devices—such as mobile phones and sensors—collaboratively train a shared global model while maintaining local data privacy. In the standard federated learning (FL) paradigm, clients independently train local models using their datasets, and a central server aggregates these locally trained models to construct a global model. Traditional aggregation approaches like FedAvg compute an element-wise average of model parameters, which, although straightforward, can result in suboptimal model performance due to the permutation invariance of neural network parameters.

Methodology

Permutation Invariance in Neural Networks

The challenge of permutation invariance arises because neural network parameters can be reordered without changing the model's functionality. Consequently, naive averaging, as performed in FedAvg, often leads to mismatched neuron alignments, diminishing the aggregated model's quality. To address this, the FedMA algorithm aligns (matches) similar neurons across local models before averaging.

Matched Averaging Formulation

The process of matched averaging involves solving a bipartite matching problem to align neurons with similar features from different clients. This alignment is formalized mathematically by an optimization problem that minimizes the sum of differences (using an appropriate similarity metric) between matched neurons. The optimization problem is solved by an iterative procedure using the Hungarian algorithm, ensuring appropriate neuron alignments across clients. This approach is extended to CNNs and LSTMs by considering channels and hidden states as elements to be matched, respectively.

Layer-wise Matching

To effectively handle deep architectures, the FedMA algorithm performs layer-wise matching. It starts by aggregating the weights of the first layer, broadcasts these weights back to clients, and then iteratively processes each subsequent layer. This ensures that each layer's neurons are correctly matched before moving on to the next, effectively reducing the communication burden and preserving model integrity.

Empirical Evaluation

The paper presents extensive empirical evaluations on various datasets, including CIFAR-10 with VGG-9 models and the Shakespeare dataset with LSTM models, under both homogeneous and heterogeneous data distributions.

1. Communication Efficiency and Convergence: FedMA demonstrated superior performance in terms of convergence speed and communication efficiency compared to FedAvg and FedProx. The matching process effectively reduced the number of communication rounds while yielding a global model with higher accuracy.
2. Effect of Local Training Epochs: The sensitivity of FedAvg and FedProx to the number of local training epochs was highlighted, with longer local training potentially leading to divergence. In contrast, FedMA showed stable performance even with extended local training, showcasing its robustness.
3. Bias Handling: FedMA also excelled in mitigating data biases, such as geographic or visual domain biases, by training each client on its domain-specific data before effective aggregation. This resulted in models that performed well across varied, previously underrepresented domains.
4. Data Efficiency: FedMA was shown to be efficient in utilizing additional data from new clients, improving model performance consistently as more clients joined the federated learning setup.

Theoretical and Practical Implications

FedMA addresses a critical challenge in federated learning by effectively matching and averaging neurons across clients, which not only enhances model performance but also maintains efficient communication. This has significant implications for practical deployments of federated learning in diverse scenarios, from mobile edge devices to large sensor networks. The algorithm’s robustness to extended local training and data heterogeneity makes it particularly suitable for real-world applications where data distribution is inherently non-iid and bandwidth is a limiting factor.

Future Directions

Future work should focus on extending FedMA to handle more complex neural network components like residual connections and batch normalization layers. Additionally, exploring connections with optimal transport literature to enhance hidden-to-hidden weight matching in LSTMs could provide further improvements. Lastly, evaluating FedMA's fault tolerance and performance on larger, more complex datasets will be imperative for broader adoption.

In summary, FedMA represents a significant step forward in federated learning, offering a balanced approach to model training and aggregation that expertly handles neural network permutation invariance. Its empirical success and theoretical soundness suggest a wide range of applications, making it an important contribution to the field of distributed machine learning.