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Attacking Provable Defenses Against Poisoning Attacks in High-Dimensional Machine Learning


Core Concepts
The authors present a new attack called HIDRA that subverts the claimed dimension-independent bias bounds of provable defenses against poisoning attacks in high-dimensional machine learning settings. HIDRA highlights a fundamental computational bottleneck in these defenses, leading to a bias that scales with the number of dimensions.
Abstract
The paper focuses on the problem of Byzantine robust aggregation, where a fraction ϵ of input vectors can be arbitrarily corrupted by an adversary during the training of machine learning models. The authors analyze the limitations of existing robust aggregation algorithms, which provide either weak bounds on the bias (dependent on the number of dimensions) or require computationally expensive operations that become infeasible in high dimensions. The key contributions are: The authors propose a new attack called HIDRA that can induce a bias matching the theoretical upper bounds of strong robust aggregators in low-dimensional settings. This shows the tightness of prior theoretical analyses. More importantly, the authors identify a fundamental computational bottleneck in the practical realization of strong robust aggregators in high dimensions. Existing defenses have to break down the high-dimensional vectors into smaller chunks to make the computations tractable. HIDRA exploits this chunking procedure to induce a near-optimal bias of Ω(√ϵd) per chunk, resulting in a total bias that scales with the number of dimensions. The authors provide a formal analysis to prove the optimality of their HIDRA attack against practical realizations of strong robust aggregators. They also show that the computational bottleneck targeted by HIDRA is fundamental to the problem of robust aggregation in general. Experimental results demonstrate that HIDRA consistently leads to a drastic drop in the accuracy of trained models, even when using state-of-the-art strong robust aggregators, in contrast to prior attacks. The paper leaves the arms race between poisoning attacks and provable defenses wide open, highlighting the challenges in designing practical and provably robust aggregation algorithms for high-dimensional machine learning.
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Quotes
"HIDRA highlights a novel computational bottleneck that has not been a concern of prior information-theoretic analysis." "Our findings leave the arms race between poisoning attacks and provable defenses wide open." "The computational bottleneck targeted by HIDRA is fundamental to the problem of robust aggregation in general, not specific to a single algorithm."

Key Insights Distilled From

by Sarthak Chou... at arxiv.org 04-22-2024

https://arxiv.org/pdf/2312.14461.pdf
Attacking Byzantine Robust Aggregation in High Dimensions

Deeper Inquiries

How can the computational bottleneck identified in this work be addressed to design more efficient and provably robust aggregation algorithms for high-dimensional machine learning

The computational bottleneck identified in the work can be addressed by exploring alternative approaches to designing more efficient and provably robust aggregation algorithms for high-dimensional machine learning. One potential solution is to investigate parallel processing techniques to distribute the computation of the maximum variance direction across multiple cores or GPUs. By leveraging parallel computing, the time complexity of computing the maximum variance direction can be significantly reduced, thereby mitigating the computational bottleneck. Another approach is to optimize the algorithmic steps involved in computing the maximum variance direction. This optimization can involve refining the iterative matrix multiplication steps or exploring more efficient algorithms for eigenvector computation. By streamlining the computational process, the overall efficiency of the robust aggregation algorithm can be improved, leading to faster and more scalable implementations. Furthermore, researchers can explore the use of approximation algorithms or heuristics to estimate the maximum variance direction with acceptable accuracy while reducing the computational complexity. Approximation techniques can provide a trade-off between computational efficiency and accuracy, making them suitable for high-dimensional settings where exact computations may be impractical. Overall, by combining parallel processing, algorithmic optimization, and approximation techniques, it is possible to address the computational bottleneck and design more efficient and provably robust aggregation algorithms for high-dimensional machine learning.

What other types of poisoning attacks (e.g., targeted or backdoor attacks) can be developed to further stress-test the limits of provable defenses against adversarial corruptions

To further stress-test the limits of provable defenses against adversarial corruptions, researchers can explore the development of targeted and backdoor poisoning attacks in addition to untargeted attacks. Targeted Poisoning Attacks: Targeted attacks aim to manipulate the model's behavior to misclassify specific classes of inputs. By crafting poisoned data samples that are strategically designed to cause misclassification of specific target classes, targeted poisoning attacks can challenge the robustness of machine learning models. These attacks can be used to evaluate the effectiveness of defense mechanisms in detecting and mitigating class-specific biases introduced by adversarial manipulations. Backdoor Poisoning Attacks: Backdoor attacks involve inserting hidden triggers or patterns into the training data that can be exploited to trigger specific behaviors in the model during inference. By injecting subtle but malicious patterns into the training data, backdoor attacks can compromise the integrity and reliability of machine learning models. Evaluating the resilience of defenses against backdoor attacks can provide insights into the robustness of the models against covert manipulations. By exploring these different types of poisoning attacks, researchers can comprehensively assess the effectiveness of provable defenses in safeguarding machine learning models against various adversarial threats and vulnerabilities.

Are there alternative approaches beyond robust aggregation that can provide provable guarantees against poisoning attacks in high-dimensional machine learning settings

Beyond robust aggregation, alternative approaches can provide provable guarantees against poisoning attacks in high-dimensional machine learning settings. Some of these approaches include: Feature Engineering and Selection: By carefully designing and selecting features that are less susceptible to adversarial manipulations, machine learning models can be made more robust against poisoning attacks. Feature engineering techniques such as dimensionality reduction, feature scaling, and feature selection can help in creating more resilient models that are less affected by adversarial corruptions. Ensemble Learning: Ensemble learning techniques, such as bagging, boosting, and stacking, can enhance the robustness of machine learning models by combining multiple base models to make predictions. By aggregating the outputs of diverse models, ensemble methods can reduce the impact of individual adversarial manipulations, thereby improving the overall resilience of the system. Adversarial Training: Adversarial training involves augmenting the training data with adversarially crafted examples to expose the model to potential attacks during the learning process. By iteratively training the model on both clean and adversarial examples, adversarial training can help in fortifying the model against poisoning attacks and improving its generalization capabilities. Certified Robustness: Certified robustness techniques provide formal guarantees on the model's resilience against adversarial perturbations. By leveraging methods such as robust optimization, interval bound propagation, and certified defenses, machine learning models can be designed to withstand adversarial attacks with provable guarantees on their robustness. By integrating these alternative approaches with robust aggregation and other defense mechanisms, it is possible to enhance the security and reliability of machine learning systems in high-dimensional settings while providing provable guarantees against poisoning attacks.
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