We seek the best traffic allocation scheme for the edge-cloud computing network that satisfies constraints and minimizes the cost based on burstable billing. First, for a fixed network topology, we formulate a family of integer programming problems with random parameters describing the various traffic demands. Then, to overcome the difficulty caused by the discrete feature of the problem, we generalize the Gumbel-softmax reparameterization method to induce an unconstrained continuous optimization problem as a regularized continuation of the discrete problem. Finally, we introduce the Gumbel-softmax sampling network to solve the optimization problems via unsupervised learning. The network structure reflects the edge-cloud computing topology and is trained to minimize the expectation of the cost function for unconstrained continuous optimization problems. The trained network works as an efficient traffic allocation scheme sampler, remarkably outperforming the random strategy in feasibility and cost function value. Besides testing the quality of the output allocation scheme, we examine the generalization property of the network by increasing the time steps and the number of users. We also feed the solution to existing integer optimization solvers as initial conditions and verify the warm-starts can accelerate the short-time iteration process. The framework is general with solid performance, and the decoupled feature of the random neural networks is adequate for practical implementations.

翻译：我们寻求满足约束条件并基于突发计费模式最小化成本的边缘-云计算网络最优流量分配方案。首先，针对固定网络拓扑，我们构建了一族包含随机参数（描述各类流量需求）的整数规划问题。然后，为克服问题离散特性带来的困难，我们将Gumbel-softmax重参数化方法推广，通过引入无约束连续优化问题作为离散问题的正则化延拓。最后，我们提出Gumbel-softmax采样网络，通过无监督学习求解优化问题。该网络结构反映边缘-云计算拓扑，并通过训练最小化无约束连续优化问题代价函数的期望值。训练后的网络可作为高效的流量分配方案采样器，在可行性与代价函数值方面显著优于随机策略。除测试输出分配方案的质量外，我们通过增加时间步长和用户数量考察网络的泛化性能。同时，将解作为初始条件输入现有整数优化求解器，验证热启动可加速短期迭代过程。该框架具有通用性与鲁棒性，随机神经网络的解耦特性足以支持实际部署。