  Greedy-GQ is a value-based reinforcement learning (RL) algorithm for optimal
control. Recently, the finite-time analysis of Greedy-GQ has been developed
under linear function approximation and Markovian sampling, and the algorithm
is shown to achieve an $\epsilon$-stationary point with a sample complexity in
the order of $\mathcal{O}(\epsilon^{-3})$. Such a high sample complexity is due
to the large variance induced by the Markovian samples. In this paper, we
propose a variance-reduced Greedy-GQ (VR-Greedy-GQ) algorithm for off-policy
optimal control. In particular, the algorithm applies the SVRG-based variance
reduction scheme to reduce the stochastic variance of the two time-scale
updates. We study the finite-time convergence of VR-Greedy-GQ under linear
function approximation and Markovian sampling and show that the algorithm
achieves a much smaller bias and variance error than the original Greedy-GQ. In
particular, we prove that VR-Greedy-GQ achieves an improved sample complexity
that is in the order of $\mathcal{O}(\epsilon^{-2})$. We further compare the
performance of VR-Greedy-GQ with that of Greedy-GQ in various RL experiments to
corroborate our theoretical findings.
