Single Timescale Actor-Critic Method to Solve the Linear Quadratic Regulator with Convergence Guarantees

We propose a single timescale actor-critic algorithm to solve the linear quadratic regulator (LQR) problem. A least squares temporal difference (LSTD) method is applied to the critic and a natural policy gradient method is used for the actor. We give a proof of convergence with sample complexity $\mathcal{O}(\varepsilon^{-1} \log(\varepsilon^{-1})^2)$. The method in the proof is applicable to general single timescale bilevel optimization problems. We also numerically validate our theoretical results on the convergence.

actor-critic algorithm complexity convergence difference gradient least linear natural policy regulator squares temporal