  The finite-time convergence of off-policy TD learning has been
comprehensively studied recently. However, such a type of convergence has not
been well established for off-policy TD learning in the multi-agent setting,
which covers broader applications and is fundamentally more challenging. This
work develops two decentralized TD with correction (TDC) algorithms for
multi-agent off-policy TD learning under Markovian sampling. In particular, our
algorithms preserve full privacy of the actions, policies and rewards of the
agents, and adopt mini-batch sampling to reduce the sampling variance and
communication frequency. Under Markovian sampling and linear function
approximation, we proved that the finite-time sample complexity of both
algorithms for achieving an $\epsilon$-accurate solution is in the order of
$\mathcal{O}(\epsilon^{-1}\ln \epsilon^{-1})$, matching the near-optimal sample
complexity of centralized TD(0) and TDC. Importantly, the communication
complexity of our algorithms is in the order of $\mathcal{O}(\ln
\epsilon^{-1})$, which is significantly lower than the communication complexity
$\mathcal{O}(\epsilon^{-1}\ln \epsilon^{-1})$ of the existing decentralized
TD(0). Experiments corroborate our theoretical findings.
