Stochastic Trajectory Influence Functions for LQR: Joint Sensitivity Through Dynamics and Noise Covariance

[2603.21539] Stochastic Trajectory Influence Functions for LQR: Joint Sensitivity Through Dynamics and Noise Covariance Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Electrical Engineering and Systems Science > Systems and Control arXiv:2603.21539 (eess) [Submitted on 23 Mar 2026 ( v1 ), last revised 14 Aug 2026 (this version, v2)] Title: Stochastic Trajectory Influence Functions for LQR: Joint Sensitivity Through Dynamics and Noise Covariance Authors: Jiachen Li , Shihao Li , Soovadeep Bakshi , Jiamin Xu , Dongmei Chen View a PDF of the paper titled Stochastic Trajectory Influence Functions for LQR: Joint Sensitivity Through Dynamics and Noise Covariance, by Jiachen Li and 4 other authors View PDF HTML (experimental) Abstract: We present a three-level influence hierarchy for data valuation in stochastic LQR. At the \emph{model level}, the trajectory influence surrogate $\IFm_k := H^{-1}g_k$ approximates the leave-one-trajectory parameter shift. At the \emph{control level} with fixed covariance, the usual fixed-noise score is obtained by composing $\IFm_k$ with the Riccati gradient of $\tr(P(\theta)\Sigma)$. At the \emph{stochastic control level}, the plug-in cost depends additionally on the residual covariance estimate $\hat W$, so removing a trajectory perturbs the cost through both the dynamics and the covariance channels. We derive an exact leave-one-trajectory decomposition of the covariance shift into a \emph{direct-removal} term and a \emph{parameter-shift} term, show that the additional first-order contribution is a simple residual cross-moment, and obtain a stochastic influence score built directly on $\IFm_k$. The resulting method preserves the amortized structure of prior work: after one Hessian factorization and one adjoint Lyapunov solve, each trajectory requires only a dot product plus an $O(n_x^2)$ direct-removal correction. The shared Hessian solves can also be performed iteratively by conjugate gradients when explicit factorization is undesirable. The new covariance remainder is explicit and does not involve Lyapunov-operator amplification; the only amplified term is the familiar Riccati remainder inherited from fixed-covariance influence analysis. Numerical results on two linear systems show that accounting for the estimated covariance substantially improves agreement with exact leave-one-trajectory retraining, especially under heterogeneous noise. Subjects: Systems and Control (eess.SY) Cite as: arXiv:2603.21539 [eess.SY] (or arXiv:2603.21539v2 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2603.21539 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jiachen Li [ view email ] [v1] Mon, 23 Mar 2026 03:51:12 UTC (677 KB) [v2] Fri, 14 Aug 2026 21:36:25 UTC (2,254 KB) Full-text links: Access Paper: View a PDF of the paper titled Stochastic Trajectory Influence Functions for LQR: Joint Sensitivity Through Dynamics and Noise Covariance, by Jiachen Li and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: eess.SY < prev | next > new | recent | 2026-03 Change to browse by: cs cs.SY eess References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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