Byzantine-Robust Federated Learning: Impact of Client Subsampling and Local Updates (2402.12780v2)

Abstract: The possibility of adversarial (a.k.a., {\em Byzantine}) clients makes federated learning (FL) prone to arbitrary manipulation. The natural approach to robustify FL against adversarial clients is to replace the simple averaging operation at the server in the standard $\mathsf{FedAvg}$ algorithm by a \emph{robust averaging rule}. While a significant amount of work has been devoted to studying the convergence of federated {\em robust averaging} (which we denote by $\mathsf{FedRo}$), prior work has largely ignored the impact of {\em client subsampling} and {\em local steps}, two fundamental FL characteristics. While client subsampling increases the effective fraction of Byzantine clients, local steps increase the drift between the local updates computed by honest (i.e., non-Byzantine) clients. Consequently, a careless deployment of $\mathsf{FedRo}$ could yield poor performance. We validate this observation by presenting an in-depth analysis of $\mathsf{FedRo}$ tightly analyzing the impact of client subsampling and local steps. Specifically, we present a sufficient condition on client subsampling for nearly-optimal convergence of $\mathsf{FedRo}$ (for smooth non-convex loss). Also, we show that the rate of improvement in learning accuracy {\em diminishes} with respect to the number of clients subsampled, as soon as the sample size exceeds a threshold value. Interestingly, we also observe that under a careful choice of step-sizes, the learning error due to Byzantine clients decreases with the number of local steps. We validate our theory by experiments on the FEMNIST and CIFAR-$10$ image classification tasks.

• The paper introduces FedRo, a robust variant of Federated Averaging that replaces simple averaging with a robust aggregation function to filter Byzantine updates.
• The authors derive sufficient conditions for client subsampling and optimal local training steps that ensure convergence despite adversarial client behavior.
• Empirical results on FEMNIST and CIFAR-10 show that careful parameter tuning enhances resilience and scalability in federated learning systems.

Tackling Byzantine Clients in Federated Learning

The paper "Tackling Byzantine Clients in Federated Learning" by Allouah et al. addresses a critical issue in federated learning (FL): robustness against Byzantine clients, which can act maliciously to disrupt the learning process. This problem is significant in FL because it involves decentralized and distributed training over multiple clients, raising the risk of adversarial behaviors that can manipulate model updates for misuse.

Core Content and Findings

The authors propose a robust variant of the Federated Averaging algorithm called FedRo, aimed at enhancing resilience against the influence of Byzantine clients. The FedRo algorithm addresses the vulnerability of the standard Federated Averaging (FedAvg) technique to such adversarial agents who can send erroneous or biased updates to the central server. A key innovation in FedRo is the replacement of the simple averaging aggregation rule with a robust aggregation function that filters out anomalies, allowing the server to mitigate the impact of malicious updates.

The paper introduces a rigorous analysis of FedRo in the context of two essential federated learning characteristics: client subsampling and local training steps. Client subsampling refers to the selection of a subset of clients in each round to participate in training, which impacts the effective proportion of Byzantines if the sampled subset is corrupted. Local steps involve multiple iterations of model updates using a client's local data before communicating back to the server.

Two main theoretical insights provided by the authors are:

1. Client Subsampling and Convergence: The authors establish sufficient conditions for the number of clients to be subsampled (denoted as n) and the maximum tolerable Byzantine clients, ensuring convergence. A detailed derivation provides thresholds for these parameters based on the Kullback-Leibler divergence, illustrating how FedRo maintains robustness.
2. The Impact of Local Steps: The results indicate that increasing local training steps (denoted as K) while keeping step sizes adequately small can reduce the asymptotic error from Byzantine clients due to averaging several stochastic gradients. This shifts the conventional view that local updates induce bias, lacking in robustness schemes without this multi-step consideration.

Performance and Practical Implications

Empirical results validate the theoretical analysis through experiments on image classification tasks such as FEMNIST and CIFAR-10 datasets. The findings underscore how careful tuning of the client subsampling and local steps can achieve robust model training even when a significant fraction of clients may be adversarial.

The paper offers practical insights into designing robust FL systems, emphasizing:

• Parameter Tuning: The derived bounds for subsampling size and Byzantine resilience furnish practitioners with clear guidelines on setting these parameters to balance robustness and efficiency.
• Algorithm Scalability: By addressing the diminishing returns of client subsampling, FedRo provides scalability in FL systems, optimizing communication overhead without significantly sacrificing model performance.
• Robustness Components: The examination of robust aggregation functions extends beyond FedRo, inviting further research into other aggregation schemes that can improve resilience in similar settings.

Future Prospects

Looking forward, the framework and findings of this paper open pathways to further narrow the robustness gap in federated learning, such as integrating privacy-preserving mechanisms while maintaining Byzantine resistance. Moreover, the dependence of robustness on the statistical heterogeneity of client data offers another dimension for future exploration, inviting richer models of adversarial behavior and client diversity in federated systems.

In conclusion, Allouah et al.'s work makes significant progress in advancing the robustness of federated learning against Byzantine threats, redefining traditional mechanisms with a focus on subsampling strategies and informed local computation steps. This holds promise not just for secure and efficient FL implementations but also for wide-ranging application fields where secure distributed computation is indispensable.