用次梯度法解决非光滑目标下的系统辨识问题，兼顾速度与收敛性。
Subgradient Method for System Identification with Non-Smooth Objectives
- 采用次梯度法处理随时间更新的非光滑优化问题。
- 在烧蚀期后实现线性收敛至真实系统参数。
- 适用于资源受限场景，适合安全关键应用研究者。
本文研究基于次梯度的算法，用于解决具有非光滑目标函数的线性时不变系统辨识问题。这在安全关键应用中对鲁棒系统辨识至关重要。尽管已有工作提供了使用优化求解器的理论精确恢复保证，但针对实际应用的快速学习算法及其收敛性设计仍待探索。本文分析了该设定下的次梯度方法，其中优化问题随新测量数据的获取而动态变化，证明了在最佳步长和Polyak步长下，经过烧蚀期后可实现对真实系统参数的线性收敛。进一步刻画了常数与递减步长下的次线性收敛性，仅需最少信息即可实现广泛适用。最后，对比了标准求解器与次梯度算法的时间复杂度，并通过实验验证了结论。这是首个分析次梯度算法在非光滑目标系统辨识中的工作。
原文摘要 · Abstract (English)
This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical applications. While existing work provides theoretical exact recovery guarantees using optimization solvers, the design of fast learning algorithms with convergence guarantees for practical use remains unexplored. We analyze the subgradient method in this setting, where the optimization problems to be solved evolve over time as new measurements are collected, and we establish linear convergence to the ground-truth system for both the best and Polyak step sizes after a burn-in period. We further characterize sublinear convergence of the iterates under constant and diminishing step sizes, which require only minimal information and thus offer broad applicability. Finally, we compare the time complexity of standard solvers with the subgradient algorithm and support our findings with experimental results. This is the first work to analyze subgradient algorithms for system identification with non-smooth objectives.
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