Sample Complexity of Linear Quadratic Regulator Without Initial Stability

Inspired by REINFORCE, we introduce a novel receding-horizon algorithm for the Linear Quadratic Regulator (LQR) problem with unknown parameters. 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 Riemannian distance over the Riccati operator. This refinement leads to a better sample complexity and ensures improved convergence guarantees. Numerical simulations validate the theoretical results, demonstrating the method's practical feasibility and performance in realistic scenarios.