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In a vehicular edge computing (VEC) system, vehicles can share their surplus computation resources to provide cloud computing services. The highly dynamic environment of the vehicular network makes it challenging to guarantee the task offloading delay. To this end, we introduce task replication to the VEC system, where the replicas of a task are offloaded to multiple vehicles at the same time, and the task is completed upon the first response among replicas. First, the impact of the number of task replicas on the offloading delay is characterized, and the optimal number of task replicas is approximated in closed-form. Based on the analytical result, we design a learning-based task replication algorithm (LTRA) with combinatorial multi-armed bandit theory, which works in a distributed manner and can automatically adapt itself to the dynamics of the VEC system. A realistic traffic scenario is used to evaluate the delay performance of the proposed algorithm. Results show that, under our simulation settings, LTRA with an optimized number of task replicas can reduce the average offloading delay by over 30% compared to the benchmark without task replication, and at the same time can improve the task completion ratio from 97% to 99.6%.