输入随机化下风险敏感LQR增益的不变性
On the invariance of risk-sensitive LQR gain under input randomization
浏览论文内容
中文总结 AI 辅助
该研究证明输入随机化下风险敏感LQR的最优增益具有不变性，无需重新计算，可推动其在隐私保护等需输入随机化的控制场景中的应用。
中文摘要 AI 辅助
本文证明了风险敏感线性二次调节器（LQR）问题的最优增益在输入随机化下具有不变性，即当控制器刻意向标称控制输入注入噪声时，该增益保持不变。初看这一结论有悖直觉，因为风险敏感LQR不满足确定性等价，且输入随机化会增大有效过程噪声。然而该增益得以保留，是因为输入噪声既会影响系统动力学，也会作用于代价函数，其对增益的总影响最终会抵消。因此，无需重新计算最优增益及其关联的Riccati递推，最优代价的增量可直接通过闭式形式计算。该结果推动了风险敏感LQR在采用输入随机化实现隐私保护或探索的场景中的应用，例如重放攻击检测的水印、差分隐私及路径积分控制等领域。
英文摘要
This paper shows that the optimal gain of the risk-sensitive linear quadratic regulator (LQR) problem is invariant under input randomization, i.e., when the controller deliberately injects noise into the nominal control input. This appears counterintuitive at first glance because certainty equivalence does not hold for risk-sensitive LQR and input randomization inflates the effective process noise. Nonetheless, the gain is preserved because the input noise enters not only the system dynamics but also the cost functional, and its total effect on the gain eventually vanishes. Consequently, the optimal gain and its associated Riccati recursion need not be recomputed, and the increment in the optimal cost can be readily evaluated in closed form. This result facilitates the use of risk-sensitive LQR in applications that employ input randomization for privacy or exploration, such as watermarking for replay attack detection, differential privacy, and path integral control.
发表机构
- Seoul National University（首尔大学）
机构由 AI 辅助整理，请以论文原文为准。
