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Comparing to cloud computing, fog computing performs computation and services at the edge of networks, thus relieving the computation burden of the data center and reducing the task latency of end devices. Computation latency is a crucial performance metric in fog computing, especially for real-time applications. In this paper, we study a peer computation offloading problem for a fog network with unknown dynamics. In this scenario, each fog node (FN) can offload their computation tasks to neighboring FNs in a time slot manner. The offloading latency, however, could not be fed back to the task dispatcher instantaneously due to the uncertainty of the processing time in peer FNs. Besides, peer competition occurs when different FNs offload tasks to one FN at the same time. To tackle the above difficulties, we model the computation offloading problem as a sequential FN selection problem with delayed information feedback. Using adversarial multi-arm bandit framework, we construct an online learning policy to deal with delayed information feedback. Different contention resolution approaches are considered to resolve peer competition. Performance analysis shows that the regret of the proposed algorithm, or the performance loss with suboptimal FN selections, achieves a sub-linear order, suggesting an optimal FN selection policy. In addition, we prove that the proposed strategy can result in a Nash equilibrium (NE) with all FNs playing the same policy. Simulation results validate the effectiveness of the proposed policy.