arXiv：cs.LG（机器学习，全量分类）· Kaito Ito, Alexandre Proutiere·· 15 小时前AI 评分35
线性系统辨识中的最优中心化主动激励
Optimal Centered Active Excitation in Linear System Identification
AI 导读
研究者提出一种基于普通最小二乘与半定规划的主动学习算法，用于线性系统辨识，可在中心化噪声激励下达到最小样本复杂度，并高效计算系统矩阵估计。该工作先给出任意主动学习算法达到指定精度与置信度所需样本复杂度的下界，再证明所提算法的上界与下界在通用常数因子内匹配，且界显式依赖状态维度等系统参数。论文已被 2026 IEEE CDC 接收。
正文
Abstract:We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity while allowing for efficient computation of an estimate of a system matrix. More specifically, we first establish lower bounds of the sample complexity for any active learning algorithm to attain the prescribed accuracy and confidence levels. Next, we derive a sample complexity upper bound of the proposed algorithm, which matches the lower bound for any algorithm up to universal factors. Our tight bounds are easy to interpret and explicitly show their dependence on the system parameters such as the state dimension.
| Comments: | 11 pages, Accepted to the 2026 IEEE Conference on Decision and Control (CDC) |
| Subjects: | Optimization and Control (math.OC); Machine Learning (cs.LG); Systems and Control (eess.SY); Machine Learning (stat.ML) |
| Cite as: | arXiv:2604.05518 [math.OC] |
| (or arXiv:2604.05518v2 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2604.05518 arXiv-issued DOI via DataCite |
Submission history
From: Kaito Ito [view email]
[v1]
Tue, 7 Apr 2026 07:16:16 UTC (155 KB)
[v2]
Thu, 1 Oct 2026 03:01:11 UTC (277 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org