This paper proposes a paradigm of uncertainty injection for training deep learning model to solve robust optimization problems. The majority of existing studies on deep learning focus on the model learning capability, while assuming the quality and accuracy of the inputs data can be guaranteed. However, in realistic applications of deep learning for solving optimization problems, the accuracy of inputs, which are the problem parameters in this case, plays a large role. This is because, in many situations, it is often costly or sometime impossible to obtain the problem parameters accurately, and correspondingly, it is highly desirable to develop learning algorithms that can account for the uncertainties in the input and produce solutions that are robust against these uncertainties. This paper presents a novel uncertainty injection scheme for training machine learning models that are capable of implicitly accounting for the uncertainties and producing statistically robust solutions. We further identify the wireless communications as an application field where uncertainties are prevalent in problem parameters such as the channel coefficients. We show the effectiveness of the proposed training scheme in two applications: the robust power loading for multiuser multiple-input-multiple-output (MIMO) downlink transmissions; and the robust power control for device-to-device (D2D) networks.

翻译：本文提出了一种不确定性注入范式，用于训练深度学习模型以解决鲁棒优化问题。现有的大多数深度学习研究聚焦于模型的学习能力，同时假设输入数据的质量与精度可以得到保证。然而，在利用深度学习解决优化问题的实际应用中，输入数据（即问题参数）的精度起着至关重要的作用。这是因为，在许多情况下，精确获取问题参数往往成本高昂甚至不可能实现，因此急需开发能够考虑输入不确定性并生成对这些不确定性具有鲁棒性的解的学习算法。本文提出了一种新型的不确定性注入方案，用于训练能够隐式考虑不确定性并生成统计上鲁棒解的机器学习模型。我们进一步将无线通信识别为一个问题参数（如信道系数）普遍存在不确定性的应用领域。我们在两个应用中展示了所提训练方案的有效性：多用户多输入多输出（MIMO）下行传输的鲁棒功率分配，以及设备到设备（D2D）网络的鲁棒功率控制。