arXiv：cs.LG· Aravinda Kanchana Ruwanpathirana, Hemant Tyagi·· 4 小时前
RobustLDS：对抗污染下的线性动力系统学习
RobustLDS: Learning linear dynamical systems under adversarial corruptions
AI 导读
研究者提出 RobustLDS，用于从长度为 T 的单一轨迹中、在部分观测被对抗异常值污染的情况下学习线性动力系统。方法基于最小截尾平方的松弛结合交替最小化算法，并提出两个利用异常值组稀疏性的估计器（惩罚与硬约束）。其中组稀疏惩罚估计器给出了非渐近误差界，实证表明所提估计器在实践中表现良好。
正文
Abstract: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.
| Comments: | 40 pages, 8 figures |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Systems and Control (eess.SY); Optimization and Control (math.OC); Statistics Theory (math.ST) |
| Cite as: | arXiv:2610.11906 [stat.ML] |
| (or arXiv:2610.11906v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.11906 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Aravinda Kanchana Ruwanpathirana [view email]
[v1]
Thu, 8 Oct 2026 13:08:25 UTC (12,291 KB)
来源：arXiv：cs.LG · arxiv.org