发表机构
Indian Institute of Science; Laboratoire de Recherche de l’EPITA（印度科学理工学院; EPITA研究实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对未知分段平稳自回归系统的最小方差控制，提出被动变化检测方法 PIECE-CD，实现对数遗憾并保证检测延迟。
AI 中文摘要
我们研究具有外生输入且系数在未知时刻变化的未知自回归系统的最小方差控制。在有界独立扰动、固定检测间隔、稳定性与可行性条件以及变化之间有足够时间间隔的条件下，我们证明了遗憾为 \\(O((C+1)\log((T+1)/\delta))\\)，概率至少为 \\(1-\delta\\)，其中 \\(T\\) 为时间范围，\\(C\\) 为变化次数。与切换赌博机不同（其中未选择的臂可能未被观察到地变化），可行的被控对象变化在利用过程中提供信息：正确的可行控制器仅在输出中留下扰动，而可检测的变化会在旧控制器下提高输出能量。PIECE-CD 在初始阶段和报警后探索，然后使用门控递归最小二乘进行控制。其能量测试将窗口化输出功率与高于噪声底限的阈值进行比较；扩展到不稳定控制器失配的情况还监控参考控制器的输入提议。我们控制整个时间范围内的误报，并证明对数检测延迟。输入被裁剪到规定的界限。对数遗憾也在一个明确条件下成立，该条件确保裁剪在有限燃烧期后变为非激活。在所述可行性条件下，扩展检测器覆盖了在固定窗口内具有可检测多余能量的失稳变化。
英文摘要
We study minimum-variance control of an unknown autoregressive system with exogenous inputs and coefficients that change at unknown times. Under bounded independent disturbances, fixed detection gaps, stability and feasibility conditions, and sufficient time between changes, we prove \(O((C+1)\log((T+1)/δ))\) regret with probability at least \(1-δ\), where \(T\) is the horizon and \(C\) the number of changes. Unlike switching bandits, where unselected arms can change unobserved, admissible plant changes provide information during exploitation: the correct feasible controller leaves only the disturbance in the output, whereas a detectable change raises output energy under the old controller. PIECE-CD explores initially and after alarms, then uses gated recursive least squares for control. Its energy test compares windowed output power with a threshold above the noise floor; the extension to unstable controller mismatches also monitors the reference controller's input proposal. We control false alarms across the horizon and prove logarithmic detection delay. Inputs are clipped to prescribed bounds. Logarithmic regret also holds under an explicit condition ensuring that clipping becomes inactive after a finite burn-in. Under the stated feasibility conditions, the extended detector covers destabilizing changes with detectable excess energy over a fixed window.
