Stochastic Trajectory Influence Functions for LQR: Joint Sensitivity Through Dynamics and Noise Covariance
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917357675347968 |
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| author | Li, Jiachen Li, Shihao Bakshi, Soovadeep Xu, Jiamin Chen, Dongmei |
| author_facet | Li, Jiachen Li, Shihao Bakshi, Soovadeep Xu, Jiamin Chen, Dongmei |
| contents | Model-based controllers learned from data have the biases and noise of their training trajectories, making it important to know which trajectories help or hurt closed-loop performance. Influence functions, widely used in machine learning for data attribution, approximate this effect through first-order parameter-shift surrogates, avoiding costly retraining. Applying them to stochastic LQR, however, is nontrivial because the cost depends on the learned dynamics through the Riccati equation, and the process-noise covariance is estimated from the same residuals. We develop a three-level influence hierarchy that accounts for both channels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21539 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Trajectory Influence Functions for LQR: Joint Sensitivity Through Dynamics and Noise Covariance Li, Jiachen Li, Shihao Bakshi, Soovadeep Xu, Jiamin Chen, Dongmei Systems and Control Model-based controllers learned from data have the biases and noise of their training trajectories, making it important to know which trajectories help or hurt closed-loop performance. Influence functions, widely used in machine learning for data attribution, approximate this effect through first-order parameter-shift surrogates, avoiding costly retraining. Applying them to stochastic LQR, however, is nontrivial because the cost depends on the learned dynamics through the Riccati equation, and the process-noise covariance is estimated from the same residuals. We develop a three-level influence hierarchy that accounts for both channels. |
| title | Stochastic Trajectory Influence Functions for LQR: Joint Sensitivity Through Dynamics and Noise Covariance |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2603.21539 |