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This research advances Local Differential Privacy by introducing a robust estimation method for multi-item users vulnerable to poisoning attacks. The proposed Randomized Projection with Clipping technique eliminates the traditional bias-variance tradeoff, allowing for tighter output spaces without sacrificing accuracy in trusted environments while significantly improving resilience against adversarial manipulation in untrusted settings. This work is critical for deploying privacy-preserving machine learning systems where data integrity must be maintained despite sophisticated threat models.
Robust Estimation of Sparse Numerical Vectors under Local Differential Privacy
arXiv:2607.27815v1 Announce Type: cross Abstract: Local differential privacy (LDP) protocols are vulnerable to poisoning attacks. Existing research have proposed efficient defense strategies for single-item users. However, in practice, a user may possess multiple items. The defense against poisoning attacks for multi-item users is challenging, because due to larger output spaces, the adversary can conduct more powerful attacks without being detected. In this paper, we address the robust sparse vector mean estimation problem, in which each user has a vector with $m$ nonzero coordinates. We propose Randomized Projection with Clipping (RPC). Firstly, the server sends a random binary vector to each user. The user then projects its local data on the vector, and clip the value to restrict the attacker's capability. To handle clipping bias, we propose a correction method based on a careful analysis that gives an exact expression of the bias. As a result, bias-variance tradeoff is no longer needed, thus the clipping threshold can be further reduced to shrink the output space and enhance robustness. We provide a rigorous theoretical guarantee of the estimation error under all possible attacks. Numerical experiments show that under trusted environments, our new method achieves comparable or better performance than existing methods, indicating that our method is already an efficient estimator in its own right. Under untrusted environments, our method is also significantly more robust to poisoning attacks.
Abstract:Local differential privacy (LDP) protocols are vulnerable to poisoning attacks. Existing research have proposed efficient defense strategies for single-item users. However, in practice, a user may possess multiple items. The defense against poisoning attacks for multi-item users is challenging, because due to larger output spaces, the adversary can conduct more powerful attacks without being detected. In this paper, we address the robust sparse vector mean estimation problem, in which each user has a vector with $m$ nonzero coordinates. We propose Randomized Projection with Clipping (RPC). Firstly, the server sends a random binary vector to each user. The user then projects its local data on the vector, and clip the value to restrict the attacker's capability. To handle clipping bias, we propose a correction method based on a careful analysis that gives an exact expression of the bias. As a result, bias-variance tradeoff is no longer needed, thus the clipping threshold can be further reduced to shrink the output space and enhance robustness. We provide a rigorous theoretical guarantee of the estimation error under all possible attacks. Numerical experiments show that under trusted environments, our new method achieves comparable or better performance than existing methods, indicating that our method is already an efficient estimator in its own right. Under untrusted environments, our method is also significantly more robust to poisoning attacks.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2607.27815 [stat.ML]
(or arXiv:2607.27815v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2607.27815 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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