Sample Complexity of Linear Quadratic Regulator Without Initial Stability

Abstract:Inspired by REINFORCE, we introduce a novel receding-horizon algorithm for the Linear Quadratic Regulator (LQR) problem with unknown dynamics. Unlike prior methods, our algorithm avoids reliance on two-point gradient estimates while maintaining the same order of sample complexity. Furthermore, it eliminates the restrictive requirement of starting with a stable initial policy, broadening its applicability. Beyond these improvements, we introduce a refined analysis of error propagation through the contraction of the Riccati operator under the Riemannian distance. This refinement leads to a better sample complexity and ensures improved convergence guarantees.

Optimization and Control (math.OC); Machine Learning (cs.LG); Systems and Control (eess.SY)

arXiv:2502.14210 [math.OC]

(or arXiv:2502.14210v4 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2502.14210 Focus to learn more arXiv-issued DOI via DataCite

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