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In this paper, we consider a mobile-edge computing system, where an accesspoint assists a mobile device (MD) to execute an application consisting ofmultiple tasks following a general task call graph. The objective is to jointlydetermine the offloading decision of each task and the resource allocationunder time-varying wireless fading channels and stochastic edge computingcapability, so that the energy-time cost (ETC) of the MD is minimized. Solvingthe problem is particularly hard due to the combinatorial offloading decisionsand the strong coupling among task executions under the general dependencymodel. Conventional numerical optimization methods are inefficient to solvesuch a problem, especially when the problem size is large. To address theissue, we propose a deep reinforcement learning (DRL) framework based on theactor-critic learning structure. In particular, the actor network utilizes aDNN to learn the optimal mapping from the input states to the binary offloadingdecision of each task. Meanwhile, by analyzing the structure of the optimalsolution, we derive a low-complexity algorithm for the critic network toquickly evaluate the ETC performance of the offloading decisions output by theactor network. With the low-complexity critic network, we can quickly selectthe best offloading action and subsequently store the state-action pair in anexperience replay memory as the training dataset to continuously improve theaction generation DNN. To further reduce the complexity, we show that theoptimal offloading decision exhibits an one-climb structure, which can beutilized to significantly reduce the search space of action generation.Numerical results show that for various types of task graphs, the proposedalgorithm achieves up to $99.1\%$ of the optimal performance whilesignificantly reducing the computational complexity compared to the existingoptimization methods.

Offloading and Resource Allocation with General Task Graph in Mobile Edge Computing: A Deep Reinforcement Learning Approach