Federated Learning of a Mixture of Global and Local Models (2002.05516v3)

Abstract: We propose a new optimization formulation for training federated learning models. The standard formulation has the form of an empirical risk minimization problem constructed to find a single global model trained from the private data stored across all participating devices. In contrast, our formulation seeks an explicit trade-off between this traditional global model and the local models, which can be learned by each device from its own private data without any communication. Further, we develop several efficient variants of SGD (with and without partial participation and with and without variance reduction) for solving the new formulation and prove communication complexity guarantees. Notably, our methods are similar but not identical to federated averaging / local SGD, thus shedding some light on the role of local steps in federated learning. In particular, we are the first to i) show that local steps can improve communication for problems with heterogeneous data, and ii) point out that personalization yields reduced communication complexity.

• The paper proposes a novel optimization formulation that balances global aggregation with personalized local updates in federated learning.
• It introduces tailored SGD variations that lower communication complexity and enable efficient convergence under non-IID data conditions.
• Extensive experiments confirm that the global-local model mixture significantly reduces communication overhead while maintaining model accuracy.

Overview of "Federated Learning of a Mixture of Global and Local Models"

This paper introduces a novel approach to federated learning (FL) that blends global and local model training, aiming to optimize both communication efficiency and model personalization for distributed, heterogeneous data environments. The primary contribution is an alternative optimization formulation and a family of stochastic gradient descent (SGD) algorithms designed to solve it efficiently.

Key Contributions and Methodology

1. New Optimization Formulation: The authors propose modeling FL as an optimization problem that strikes a balance between a global model trained on aggregate data from multiple devices and individual local models tailored to device-specific data. This formulation lifts the problem space from $\mathbb{R}^d$ to $\mathbb{R}^{nd}$, enabling each device to maintain personalized models.
2. Algorithm Design: Several variations of SGD are developed, including those accommodating partial participation and variance reduction. These methods seek to optimize communication complexity, a critical factor in FL systems where communication can be costly or constrained.
3. Communication Complexity and Theoretical Guarantees: The paper rigorously establishes communication complexity bounds for the proposed methods. It proves that under heterogeneous data conditions, where traditional FL methods might struggle with efficient convergence, local steps can reduce necessary communication. In particular, it is shown that by personalizing models within this new optimization framework, significant reductions in communication overhead can be achieved.
4. Personalization and Freedom from Data Homogeneity Assumptions: The paper argues experimentally and analytically that personalized FL does not require data similarity assumptions. This is critical since data distributions across devices in real-world applications (like mobile phones or IoT devices) are often heterogeneous.
5. Empirical Validation: Extensive experiments demonstrate that the proposed methods yield faster convergence with fewer communication rounds compared to conventional methods, especially under non-IID data distributions. The numerical results support the theoretical predictions, highlighting the utility of slightly personalized models in reducing the communication burden without compromising model accuracy.

Implications and Future Directions

This paper has substantial implications for both theoretical and practical aspects of federated learning:

• Theoretical Insights: By introducing and analyzing a mixture model formulation for FL, the paper shifts the research focus from the pursuit of a single global model to a paradigm where personalized and collaboratively trained models coexist. This approach acknowledges diverse user data distributions while maintaining the advantages of data privacy inherent to FL.
• Practical Impacts: The reduction in communication complexity can extend the applicability of FL to environments with limited connectivity or costly data transmission, such as rural or remote areas. Personalized models may also enhance user experience by aligning more closely with individual data characteristics.
• Future Research Directions: Future work could explore adaptive optimization frameworks where the trade-off parameter between global and local models is dynamically set based on real-time data properties or user needs. Further, integrating differential privacy mechanisms seamlessly into this framework could ensure robust security without excessive computational overhead.

In conclusion, this paper provides a compelling alternative to standard approaches in federated learning, with theoretical and empirical evidence affirming its potential to transform how models are trained in decentralized settings. It prompts a reassessment of how local models should interact with global objectives, particularly in the context of varied and complex data environments.