Sample Complexity of the Linear Quadratic Regulator: A Reinforcement Learning Lens
This work addresses a fundamental challenge in reinforcement learning for control systems by providing a more efficient and practical algorithm for policy optimization in LQR problems.
The authors tackled the problem of learning an optimal controller for linear quadratic regulators with unknown parameters, achieving an ε-optimal solution with Õ(1/ε) function evaluations, which improves upon prior rates of Õ(1/ε²) without relying on unrealistic two-point gradient estimates.
We provide the first known algorithm that provably achieves $\varepsilon$-optimality within $\widetilde{\mathcal{O}}(1/\varepsilon)$ function evaluations for the discounted discrete-time LQR problem with unknown parameters, without relying on two-point gradient estimates. These estimates are known to be unrealistic in many settings, as they depend on using the exact same initialization, which is to be selected randomly, for two different policies. Our results substantially improve upon the existing literature outside the realm of two-point gradient estimates, which either leads to $\widetilde{\mathcal{O}}(1/\varepsilon^2)$ rates or heavily relies on stability assumptions.