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

TL;DR

This paper introduces a novel influence function framework for stochastic LQR that captures the effects of both dynamics and noise covariance on control performance, enabling better trajectory attribution.

Contribution

It develops a three-level influence hierarchy that jointly considers dynamics and noise covariance effects in stochastic LQR, extending influence functions to this setting.

Findings

Effective attribution of trajectory influence in stochastic LQR.

Enhanced understanding of noise and dynamics impact on control performance.

Framework applicable to data-driven control systems.

Abstract

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.