Exploiting Shared Representations for Personalized Federated Learning (2102.07078v3)

Abstract: Deep neural networks have shown the ability to extract universal feature representations from data such as images and text that have been useful for a variety of learning tasks. However, the fruits of representation learning have yet to be fully-realized in federated settings. Although data in federated settings is often non-i.i.d. across clients, the success of centralized deep learning suggests that data often shares a global feature representation, while the statistical heterogeneity across clients or tasks is concentrated in the labels. Based on this intuition, we propose a novel federated learning framework and algorithm for learning a shared data representation across clients and unique local heads for each client. Our algorithm harnesses the distributed computational power across clients to perform many local-updates with respect to the low-dimensional local parameters for every update of the representation. We prove that this method obtains linear convergence to the ground-truth representation with near-optimal sample complexity in a linear setting, demonstrating that it can efficiently reduce the problem dimension for each client. This result is of interest beyond federated learning to a broad class of problems in which we aim to learn a shared low-dimensional representation among data distributions, for example in meta-learning and multi-task learning. Further, extensive experimental results show the empirical improvement of our method over alternative personalized federated learning approaches in federated environments with heterogeneous data.

Exploiting Shared Representations for Personalized Federated Learning

Overview

The paper introduces an innovative framework, Federated Representation Learning (FedRep), designed to address data heterogeneity in federated learning environments. Unlike traditional federated learning models that strive to create a single shared model across all clients, FedRep identifies and exploits a shared data representation while allowing clients to maintain unique local heads. This approach significantly enhances model performance in environments characterized by diverse data distributions across clients.

Key Contributions

The primary contributions of the paper can be categorized as follows:

1. FedRep Algorithm: The algorithm leverages gradient-based updates to learn a global low-dimensional representation using data from all clients. Each client computes a personalized classifier, or "head," tailored to its local data labels, improving both personalization and efficiency.
2. Optimization in Linear Settings: The paper provides theoretical evidence that FedRep achieves linear convergence to the ground-truth representation in linear regression tasks. This convergence is achieved with an efficient sample complexity, indicating the algorithm's ability to reduce problem dimensionality effectively.
3. Empirical Validation: Through comprehensive experiments on synthetic data and real datasets (CIFAR10, CIFAR100, FEMNIST, Sent140), FedRep demonstrates superior performance over several baseline approaches, particularly in environments with data heterogeneity.

Numerical and Theoretical Insights

FedRep showcases robust numerical results. The algorithm converges exponentially fast to a ground-truth representation, with sample complexity scaling as $$\mathcal{O}((\frac{k}{rn} + \log(n))\log(\frac{1}{\epsilon}))$$. This suggests significant improvements in sample efficiency compared to models that do not exploit shared representations. Additionally, FedRep facilitates substantial local updates, enhancing the personalization of client models and supporting effective generalization to new clients.

Implications and Future Directions

The implications of this research extend beyond federated learning. The concept of identifying a shared representation to improve individual task performance resonates with broader contexts, such as meta-learning and multi-task learning. The alternating minimization-descent approach discussed could lead to new solutions in representation learning, ensuring that models are more adaptable and efficient in high-dimensional settings.

Future research could explore the extension of FedRep to non-linear settings, potentially unlocking further efficiencies and broader applicability. Additionally, further theoretical analyses on the convergence properties in more complex networks could solidify FedRep's standing as a foundational approach in personalized federated learning.

Conclusion

This paper contributes significantly to the personalized federated learning domain by presenting a novel approach that harmonizes global data insight with local client specificity. By exploiting shared representations, FedRep not only addresses data heterogeneity challenges but also paves the way for more nuanced and efficient federated learning systems.