In this paper, we present a novel learning-aided energy management scheme (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 perturbed dual learning. LEM does not require any statistical information of the system dynamics for implementation, and efficiently resolves the challenging energy outage problem. We show that LEM achieves the near-optimal [O(ϵ), O(log(1/ϵ)²)] utility-delay tradeoff with an O(1/ϵ^1-c/2) energy buffers (c ∈ (0, 1)). More interestingly, LEM possesses a convergence time of O(1/ϵ^1-c/2 + 1/ϵ^c), which is much faster than the 8(1/ϵ) time of pure queue-based techniques or the 8(1/ϵ²) time of approaches that rely purely on learning the system statistics. This fast convergence property makes LEM more adaptive and efficient in resource allocation in dynamic environments. The design and analysis of 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.