Federated Multi-Task Learning under a Mixture of Distributions (2108.10252v4)

Abstract: The increasing size of data generated by smartphones and IoT devices motivated the development of Federated Learning (FL), a framework for on-device collaborative training of machine learning models. First efforts in FL focused on learning a single global model with good average performance across clients, but the global model may be arbitrarily bad for a given client, due to the inherent heterogeneity of local data distributions. Federated multi-task learning (MTL) approaches can learn personalized models by formulating an opportune penalized optimization problem. The penalization term can capture complex relations among personalized models, but eschews clear statistical assumptions about local data distributions. In this work, we propose to study federated MTL under the flexible assumption that each local data distribution is a mixture of unknown underlying distributions. This assumption encompasses most of the existing personalized FL approaches and leads to federated EM-like algorithms for both client-server and fully decentralized settings. Moreover, it provides a principled way to serve personalized models to clients not seen at training time. The algorithms' convergence is analyzed through a novel federated surrogate optimization framework, which can be of general interest. Experimental results on FL benchmarks show that our approach provides models with higher accuracy and fairness than state-of-the-art methods.

Federated Multi-Task Learning under a Mixture of Distributions

The paper presented outlines a framework for federated multi-task learning (MTL) under an assumption of data distributions that are mixtures of unknown underlying distributions. The authors tackle prominent challenges in Federated Learning (FL), a method that allows for collaborative model training without sharing localized data, by focusing on the inherent statistical heterogeneity of local data distributions. This paper is pivotal for researchers in FL, offering insights into personalized model training across heterogeneous datasets, addressing both theoretical advancements and practical implementations.

Key Contributions

1. Mixture of Distributions Assumption: The paper proposes that each client's data distribution can be considered a mixture of several underlying distributions. This assumption allows for a flexible and comprehensive framework that supports many previous personalized FL approaches.
2. Federated EM Algorithms: Based on the above assumption, the authors develop algorithms akin to the Expectation-Maximization (EM) approach that operate in both centralized (client-server) and fully decentralized settings. These algorithms are shown to converge effectively, which is proven through a novel surrogate optimization framework. Importantly, this framework extends the capability of personalization to clients not part of the initial training phase.
3. Numerical and Fairness Improvements: Experimental validations are provided that demonstrate improved model accuracy and client fairness over state-of-the-art FL methods. The evaluation is conducted across several standardized datasets, showcasing the general applicability of the approach.

Detailed Analysis

The authors begin by examining the limitations of a single global model in federated scenarios, where data heterogeneity is predominant. Current methods, such as those iterating towards a global model fine-tuned locally (FedAvg and FedProx), often fail to cater to the specificities of clients with non-iid data.

Building on these challenges, the paper proposes a generative model assumption where local client data is a mixture of distributions. Consequently, the EM-like algorithm iteratively estimates these mixture components, effectively creating personalized models by capturing intricate relationships among data points across different clients.

1. EM Algorithm Architecture: The expectation step evaluates the component responsibilities for each data sample, while the maximization step updates the model parameters to maximize these responsibilities. The framework is flexible enough to adapt these procedures in both centralized and decentralized environments.
2. Surrogate Optimization Framework: This novel framework underpins the convergence proofs for the proposed algorithms. It represents a generalized form of optimization that allows clients to compute personalized first-order surrogate functions, facilitating effective convergence even under federated settings.
3. Convergence and Performance: Through rigorous mathematical proofs, it's demonstrated that the proposed federated optimization algorithm converges to a stationary point. Experimental results substantiate an increase in average test accuracy and fairness, measured by the distribution of performance across clients.

Implications and Future Work

The implications of this paper are manifold. Practically, the ability to generalize and personalize model learning across diverse decentralized environments without data centralization aligns with privacy-preserving goals crucial for applications involving personal data (e.g., smartphone apps, IoT devices). Theoretically, the surrogate optimization framework sets a substantial basis for further exploration into FL with robust convergence properties.

Future research could delve into further reducing computational burden and communication costs inherent in federated settings. Additionally, extending this work to incorporate rigorous privacy constraints, possibly integrating differential privacy techniques, would enhance the applicability of federated personalized learning in sensitive domains.

In conclusion, this paper successfully extends the boundaries of federated learning by introducing a robust method for personalized model training under the realistic assumption of mixed data distributions, complementing existing approaches and setting the stage for future advancements in the field.