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<p>Statistical analysis in the big-data era often faces two challenges: limited data sharing across agents, and adversarial contamination of observations. To address these dual challenges, this paper introduces a distributed learning framework designed for the adversarial contamination setting. We propose a novel approximate Newton-type surrogate loss function, which decouples the process of contamination detection from that of parameter updates. Based on this loss, we develop a dynamically regularized algorithm that employs a decreasing hard thresholding operator to identify contaminated observations. The proposed algorithm achieves efficiency in both communication and computation. Theoretical results establish minimax optimality of the resulting estimator. Furthermore, in the high-dimensional sparse setting, our estimator exhibits signal adaptivity and strong oracle properties, which in turn imply asymptotic inference. Both numerical simulations and real data analysis confirm the superiority of our framework. We finally discuss the distinction between sample-level contamination and Byzantine failures, and outline possible extensions of the proposed approach to settings in which both types of corruption coexist.</p>

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Distributed learning with adversarial contamination: an efficient and optimal approach based on dynamic regularization

  • 期刊论文

  • 发表日期：

    2026年5月27日

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  • Shixiang Liu,
  • Delin Zhao,
  • Hanming Yang

摘要

Statistical analysis in the big-data era often faces two challenges: limited data sharing across agents, and adversarial contamination of observations. To address these dual challenges, this paper introduces a distributed learning framework designed for the adversarial contamination setting. We propose a novel approximate Newton-type surrogate loss function, which decouples the process of contamination detection from that of parameter updates. Based on this loss, we develop a dynamically regularized algorithm that employs a decreasing hard thresholding operator to identify contaminated observations. The proposed algorithm achieves efficiency in both communication and computation. Theoretical results establish minimax optimality of the resulting estimator. Furthermore, in the high-dimensional sparse setting, our estimator exhibits signal adaptivity and strong oracle properties, which in turn imply asymptotic inference. Both numerical simulations and real data analysis confirm the superiority of our framework. We finally discuss the distinction between sample-level contamination and Byzantine failures, and outline possible extensions of the proposed approach to settings in which both types of corruption coexist.