  In this paper, we present a novel learning-aided energy management scheme
($\mathtt{LEM}$) for multihop energy harvesting networks. Different from prior
works on this problem, our algorithm explicitly incorporates information
learning into system control via a step called \emph{perturbed dual learning}.
$\mathtt{LEM}$ does not require any statistical information of the system
dynamics for implementation, and efficiently resolves the challenging energy
outage problem. We show that $\mathtt{LEM}$ achieves the near-optimal
$[O(\epsilon), O(\log(1/\epsilon)^2)]$ utility-delay tradeoff with an
$O(1/\epsilon^{1-c/2})$ energy buffers ($c\in(0,1)$). More interestingly,
$\mathtt{LEM}$ possesses a \emph{convergence time} of $O(1/\epsilon^{1-c/2}
+1/\epsilon^c)$, which is much faster than the $\Theta(1/\epsilon)$ time of
pure queue-based techniques or the $\Theta(1/\epsilon^2)$ time of approaches
that rely purely on learning the system statistics. This fast convergence
property makes $\mathtt{LEM}$ more adaptive and efficient in resource
allocation in dynamic environments. The design and analysis of $\mathtt{LEM}$
demonstrate how system control algorithms can be augmented by learning and what
the benefits are. The methodology and algorithm can also be applied to similar
problems, e.g., processing networks, where nodes require nonzero amount of
contents to support their actions.
