Uncertainty Injection: A Deep Learning Method for Robust Optimization. (arXiv:2302.12304v1 [cs.LG])

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.