RSA: Byzantine-Robust Stochastic Aggregation Methods for Distributed Learning from Heterogeneous Datasets (1811.03761v2)

Abstract: In this paper, we propose a class of robust stochastic subgradient methods for distributed learning from heterogeneous datasets at presence of an unknown number of Byzantine workers. The Byzantine workers, during the learning process, may send arbitrary incorrect messages to the master due to data corruptions, communication failures or malicious attacks, and consequently bias the learned model. The key to the proposed methods is a regularization term incorporated with the objective function so as to robustify the learning task and mitigate the negative effects of Byzantine attacks. The resultant subgradient-based algorithms are termed Byzantine-Robust Stochastic Aggregation methods, justifying our acronym RSA used henceforth. In contrast to most of the existing algorithms, RSA does not rely on the assumption that the data are independent and identically distributed (i.i.d.) on the workers, and hence fits for a wider class of applications. Theoretically, we show that: i) RSA converges to a near-optimal solution with the learning error dependent on the number of Byzantine workers; ii) the convergence rate of RSA under Byzantine attacks is the same as that of the stochastic gradient descent method, which is free of Byzantine attacks. Numerically, experiments on real dataset corroborate the competitive performance of RSA and a complexity reduction compared to the state-of-the-art alternatives.

• The paper introduces RSA, a novel robust stochastic subgradient method that mitigates Byzantine faults in distributed learning.
• It incorporates ℓp-norm regularization to achieve near-optimal convergence even with heterogeneous, non-iid data from potentially malicious workers.
• Empirical validation on the MNIST dataset shows RSA's competitive accuracy and lower computational complexity compared to state-of-the-art approaches.

Byzantine-Robust Stochastic Aggregation Methods for Distributed Learning

The paper "RSA: Byzantine-Robust Stochastic Aggregation Methods for Distributed Learning from Heterogeneous Datasets" addresses a significant challenge in distributed machine learning, particularly in federated learning environments. It proposes a novel class of robust stochastic subgradient methods, termed Byzantine-Robust Stochastic Aggregation (RSA), to improve learning reliability amidst Byzantine faults. These faults occur when some workers may act maliciously or erratically, sending incorrect data to the master node, thereby compromising the learning process.

Key Contributions

The paper details several contributions to the field of distributed learning:

1. Algorithm Design: The RSA methods incorporate a regularization term into the objective function. This design aims to mitigate the influence of Byzantine workers, which do not require the assumption of independent and identically distributed (i.i.d.) data across workers. This characteristic is particularly important for applications that deal with heterogeneous data.
2. Theoretical Analysis: The authors rigorously prove that RSA converges to a near-optimal solution. Notably, RSA maintains the convergence rate akin to stochastic gradient descent (SGD) even under Byzantine attacks. The learning error is shown to be dependent on the number of Byzantine workers.
3. Numerical Validation: Comprehensive experiments using the MNIST dataset demonstrate RSA's competitive accuracy under adversarial conditions compared to state-of-the-art alternatives. Moreover, RSA exhibits lower computational complexity, positioning it as an efficient solution for robust distributed learning.

Methodology

The RSA framework diverges from traditional SGD approaches by focusing not only on gradient aggregation but also on robust model aggregation. This strategy addresses the vulnerabilities in federated learning concerning data heterogeneity and Byzantine robustness. RSA introduces $\ell_p$-norm regularization in the optimization problem, which is solved using a modified version of SGD. Through theoretical discussions, it is shown that:

• For an adequately chosen regularization parameter $\lambda$, RSA can achieve consensus among worker updates, ensuring robustness against arbitrary Byzantine behaviors.
• The sub-optimal gap in RSA is quadratically dependent on the number of Byzantine workers, reflecting a controlled trade-off between robustness and accuracy.

Implications and Future Directions

The implications of this research are multifaceted. Practically, RSA can be readily adopted in federated learning scenarios, where device-level data heterogeneity and security concerns are prevalent. Theoretically, this work opens pathways for further exploration in robust optimization under more relaxed assumptions and diverse attack models.

Future research could investigate the following areas:

• Algorithmic Enhancements: Further optimizing RSA's parameters and exploring other regularization norms could enhance the robustness and performance of the algorithms.
• Scalability: Extending RSA to even larger federated learning systems with tens of thousands of devices while maintaining computational efficiency.
• Advanced Byzantine Models: Developing new strategies to counter emerging complex Byzantine strategies, potentially incorporating machine learning-based detection mechanisms.

By presenting a robust, efficient methodology for distributed machine learning, this paper makes a significant contribution to ensuring the integrity and reliability of learning systems in adversarial environments. Future advancements built upon this work are poised to address the evolving challenges in secure and efficient distributed learning.