This work explores how to leverage the historical information of the system to assist decision-making in task offloading and resource allocation problem. The objective is to achieve higher network computing rates and lower cloud-edge service costs while subjecting to the conditions of stable task queues and power constraints. Initially, an algorithm without predictive assistance is briefly introduced. However, it cannot utilize predictive information. Subsequently, a multi-frame optimization problem was constructed to leverage predictive information provided by the long short-term memory model, and heuristic information was provided by the pretrained neural network from the algorithm without predictive assistance. We employed a heuristic search algorithm to search for solutions that are better than those obtained by the non-predictive auxiliary algorithm. Finally, numerical simulations demonstrate that the predictive algorithm performs better to a certain extent when dealing with randomly generated information that exhibits strong temporal characteristics.