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In fog-assisted IoT systems, it is a common practice to offload tasks from IoT devices to their nearby fog nodes to reduce task processing latencies and energy consumptions. However, the design of online energy-efficient scheme is still an open problem because of various uncertainties in system dynamics such as processing capacities and transmission rates. Moreover, the decision-making process is constrained by resource limits on fog nodes and IoT devices, making the design even more complicated. In this paper, we formulate such a task offloading problem with unknown system dynamics as a combinatorial multi-armed bandit (CMAB) problem with long-term constraints on time-averaged energy consumptions. Through an effective integration of online learning and online control, we propose a \textit{Learning-Aided Green Offloading} (LAGO) scheme. In LAGO, we employ bandit learning methods to handle the exploitation-exploration tradeoff and utilize virtual queue techniques to deal with the long-term constraints. Our theoretical analysis shows that LAGO can reduce the average task latency with a tunable sublinear regret bound over a finite time horizon and satisfy the long-term time-averaged energy constraints. We conduct extensive simulations to verify such theoretical results.