Fall of Empires: Breaking Byzantine-tolerant SGD by Inner Product Manipulation (1903.03936v1)

Abstract: Recently, new defense techniques have been developed to tolerate Byzantine failures for distributed machine learning. The Byzantine model captures workers that behave arbitrarily, including malicious and compromised workers. In this paper, we break two prevailing Byzantine-tolerant techniques. Specifically we show robust aggregation methods for synchronous SGD -- coordinate-wise median and Krum -- can be broken using new attack strategies based on inner product manipulation. We prove our results theoretically, as well as show empirical validation.

• The paper introduces an inner product manipulation attack that reverses gradient descent by forcing the aggregated gradient's inner product to become negative.
• It exposes vulnerabilities in coordinate-wise median and Krum methods, showing their failure under near-zero gradient expectations and adversarially clustered gradients.
• Empirical results on CIFAR-10 demonstrate that such attacks significantly slow convergence and degrade accuracy, highlighting the need to redefine Byzantine tolerance.

Overview of "Fall of Empires: Breaking Byzantine-tolerant SGD by Inner Product Manipulation"

This paper by Cong Xie, Sanmi Koyejo, and Indranil Gupta from the University of Illinois Urbana-Champaign presents an analysis of vulnerabilities within Byzantine-tolerant strategies employed in distributed Stochastic Gradient Descent (SGD) frameworks. The paper critiques two prominent Byzantine robust techniques—coordinate-wise median and Krum—by introducing an attack paradigm based on inner product manipulation, which undermines the perceived robustness of these aggregation methods in adversarial environments.

Key Contributions

1. Inner Product Manipulation Attack: The authors introduce a novel class of attacks targeting the inner product between the true gradient and the aggregated vector. This attack strives to make the inner product negative, thus effectively sabotaging the gradient descent direction and hindering convergence.
2. Vulnerability Analysis of Coordinate-wise Median:
   • The paper highlights that the coordinate-wise median approach fails to maintain robustness under specific conditions where the expectation of the gradient is near-zero and the variance remains non-negligible.
   • A theoretical argument is provided to demonstrate the capacity of this method to be directed towards arbitrary results, even when theoretical guarantees like distance bounding hold.
3. Failure of Krum Under Adversarial Conditions:
   • Krum, an alternative aggregation method, is shown to be susceptible to crafted attacks with carefully calculated adversarial gradients.
   • The paper's results indicate that although Krum assumes certain variance and bounded conditions for operation, these can be circumvented by non-trivial Byzantine manipulations, particularly when worker gradients formed clusters around the mean.
4. Proposed Redefinition of Byzantine Tolerance in SGD:
   • The authors argue for a redefined concept of Byzantine tolerance in distributed SGD by emphasizing the importance of maintaining a positive inner product between the true and aggregated gradient vectors, thus ensuring valid descent direction.
5. Empirical Validation:
   • Through empirical studies conducted on a CIFAR-10 image classification task, the research substantiates the theoretical insights by demonstrating how existing methods can be disrupted by inner product manipulation attacks.
   • The experiments reveal that under attack, converged models employing coordinate-wise median and Krum falter, resulting in substantial degradation in both convergence speed and model accuracy.

Implications and Future Directions

The findings in this research offer a critical lens through which to examine the current safeguarding mechanisms in distributed machine learning against Byzantine faults. While acknowledging the significance of bounded distance rules, this paper shifts focus to more nuanced metrics like inner product positivity to better capture the essence of functional robustness in gradient descent methods.

Recognizing this vulnerability presents opportunities to innovate more resilient methods for Byzantine fault-tolerant learning. Future work could explore alternative aggregation methods or hybrid strategies that integrate robustness to inner product manipulation within Byzantine environments. Emphasis might also be on developing comprehensive defense frameworks that combine robust statistics with dynamic adaptability to adversarial signals.

By highlighting these shortcomings in state-of-the-art methods, the paper provides a foundational step towards redefining and improving defense strategies in distributed machine learning architectures, ensuring that safeguards are not merely theoretically sound but also practically impenetrable.