  Reinforcement learning (RL) has been successfully used to solve many
continuous control tasks. Despite its impressive results however, fundamental
questions regarding the sample complexity of RL on continuous problems remain
open. We study the performance of RL in this setting by considering the
behavior of the Least-Squares Temporal Difference (LSTD) estimator on the
classic Linear Quadratic Regulator (LQR) problem from optimal control. We give
the first finite-time analysis of the number of samples needed to estimate the
value function for a fixed static state-feedback policy to within
$\varepsilon$-relative error. In the process of deriving our result, we give a
general characterization for when the minimum eigenvalue of the empirical
covariance matrix formed along the sample path of a fast-mixing stochastic
process concentrates above zero, extending a result by Koltchinskii and
Mendelson in the independent covariates setting. Finally, we provide
experimental evidence indicating that our analysis correctly captures the
qualitative behavior of LSTD on several LQR instances.
