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To facilitate the deployment of private industrial Internet-of-Things (IoT), applying long-term-evolution (LTE) over unlicensed spectrum (LTE-U) is a promising technology, which can deal with the licensed spectrum scarcity problem and the stringent quality-of-service (QoS) requirement via centralized control. In this paper, we investigate the computing offloading problem for LTE-U-enabled IoT, where computing tasks on an IoT device are either executed locally or offloaded to the edge server on an LTE-U base station. Considering a constrained edge computing cost (e.g., operation power consumption) for offloaded tasks, the task scheduling problem is formulated as a constrained Markov decision process (CMDP) to maximize the long-term average reward, which integrates both task completion profit and task completion delay. In order to address the uncertainty of task arrivals and channel availability, a constrained …