发表机构
Division of Mathematical Sciences, SPMS, NTU Singapore（南洋理工大学数学科学系，SPMS）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对对抗性污染下的线性动态系统学习问题，提出结合最小截平方松弛与交替最小化的估计量，以及利用异常值组稀疏性的估计量，推导了非渐近误差界并通过实验验证了有效性。
AI 中文摘要
我们研究从长度为$T$的单条轨迹中学习受对抗性污染的线性动态系统的问题。线性动态系统的辨识本身已被广泛研究，但对抗性污染下的鲁棒系统辨识问题相对较少被探索。本工作中，我们研究$T$个观测值中有一部分被对抗性异常值污染的场景，提出基于最小截平方松弛的不同估计量，以及交替最小化算法；还提出两个利用异常值组稀疏性（通过惩罚或硬约束）的估计量，对带组稀疏惩罚的估计量推导了非渐近误差界，证明其对异常值的鲁棒性，且通过实验表明所提估计量在实际中表现良好。
英文摘要
We consider the problem of learning linear dynamical systems under adversarial contamination from a single trajectory of length $T$. While identification of linear dynamical systems itself is well-studied, the problem of robust system identification under adversarial contamination is relatively less explored. In this work, we study the setting where a fraction of the $T$ observations are contaminated by adversarial outliers. We propose different estimators based on relaxations of least-trimmed squares along with an alternating minimization algorithm. Furthermore, we also propose two estimators which exploit the group-sparsity (through penalization/hard-constraints) of the outliers. For the estimator with group-sparse penalty, we derive non-asymptotic error bounds which establish its robustness to outliers. We also show empirically that the proposed estimators work well in practice.
Comments40 pages, 8 figures
