Robust Federated Learning in a Heterogeneous Environment (1906.06629v2)

Abstract: We study a recently proposed large-scale distributed learning paradigm, namely Federated Learning, where the worker machines are end users' own devices. Statistical and computational challenges arise in Federated Learning particularly in the presence of heterogeneous data distribution (i.e., data points on different devices belong to different distributions signifying different clusters) and Byzantine machines (i.e., machines that may behave abnormally, or even exhibit arbitrary and potentially adversarial behavior). To address the aforementioned challenges, first we propose a general statistical model for this problem which takes both the cluster structure of the users and the Byzantine machines into account. Then, leveraging the statistical model, we solve the robust heterogeneous Federated Learning problem \emph{optimally}; in particular our algorithm matches the lower bound on the estimation error in dimension and the number of data points. Furthermore, as a by-product, we prove statistical guarantees for an outlier-robust clustering algorithm, which can be considered as the Lloyd algorithm with robust estimation. Finally, we show via synthetic as well as real data experiments that the estimation error obtained by our proposed algorithm is significantly better than the non-Byzantine-robust algorithms; in particular, we gain at least by 53\% and 33\% for synthetic and real data experiments, respectively, in typical settings.

• The paper introduces a 3-stage federated learning algorithm combining local empirical risk minimization, robust clustering with sub-Gaussian models, and Byzantine-resilient optimization.
• The methodology provides theoretical performance bounds, ensuring estimates competitive with oracle outcomes under typical federated learning constraints.
• Empirical results on synthetic and real-world datasets, including a 53% improvement in synthetic settings, underscore the practical viability of the proposed approach.

Insights into Robust Federated Learning in a Heterogeneous Environment

Federated Learning (FL) represents a strategic shift in distributed machine learning by enabling model training on decentralized data stored across multiple devices. As proposed in the examined paper by Ghosh et al., the distributed nature of FL faces significant challenges, primarily due to heterogeneous data distributions and Byzantine faults from worker devices. Addressing these obstacles is critical for reliable and robust model development in distributed environments, where data heterogeneity arises naturally and Byzantine failures could emanate from adversarial participants or hardware faults.

The paper offers a comprehensive solution with a clear mathematical framework, introducing a modular approach to tackle these issues. The authors propose a 3-stage algorithm, which includes local empirical risk minimization, clustering using robust estimation techniques, and executing Byzantine-resilient distributed optimization. The implementation of this approach ensures that model development in FL maintains resilience against data and compute node variability and potential adversarial threats.

Theoretical Contributions and Implications

The theoretical underpinning of the paper is significant, introducing a robust clustering mechanism leveraging sub-Gaussian mixture models and extending the classical Lloyd's algorithm to address adversarial noise. The authors derive guarantees for the proposed method under typical FL constraints, providing performance bounds on the estimation error that are competitive with those achievable by an oracle clairvoyant of the true data cluster boundaries. These bounds are notably optimal concerning key parameters such as dimension, sample size, and level of adversarial device participation.

Primary to the innovation in clustering is the adaptation of robust mean estimation techniques, such as trimmed means and iterative filtering, which are crucial in high dimensions where traditional methods like geometric medians may fall short. The implications here reach beyond theoretical interest: They provide a scalable path to robust FL algorithms applicable across various domains, from mobile device data aggregation to large-scale sensor networks.

Numerical Results

The empirical evidence presented, evaluated on both synthetic and real-world datasets—such as the Yahoo! Learning to Rank dataset—substantively endorses the theoretical promises. The implementation demonstrates marked improvement over non-robust and conventional methods, by at least 53% on synthetic settings. This validation underscores the practical relevance of algorithmic robustness, bringing future real-world deployments of FL closer to feasibility.

Future Directions

The proposed framework opens several avenues for further research. The enhancibility of the clustering step, especially in the context of higher dimensions and non-sub-Gaussian noise, warrants exploration. Moreover, extending these techniques to non-convex loss landscapes, which often arise in deep learning applications, would significantly increase the framework's utility.

Conclusion

In summary, the paper by Ghosh et al. stands as a substantial contribution in the area of distributed ML through FL. Its modular algorithm design, cemented by solid theoretical guarantees, not only advances our understanding of robust learning in heterogeneous environments but also sets the stage for practical innovations in secure and efficient federated systems. The work encourages active engagement with issues of privacy-preserving computation and contributes to the integral field of distributed optimization under uncertainty, bridging statistical learning concepts with applied machine learning advancements.