# Uncertainty Injection: A Deep Learning Method for Robust Optimization

arXiv: https://arxiv.org/abs/2302.12304 · HTML: https://mlsanity.com/paper/2302.12304/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 71 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Deeply-Supervised Nets](https://mlsanity.com/paper/1409.5185/) (2014)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [Learning Visual Features from Large Weakly Supervised Data](https://mlsanity.com/paper/1511.02251/) (2015)
- [Deep Learning is Robust to Massive Label Noise](https://mlsanity.com/paper/1705.10694/) (2017)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Towards Deep Neural Network Architectures Robust to Adversarial Examples](https://mlsanity.com/paper/1412.5068/) (2014)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Learning From Noisy Large-Scale Datasets With Minimal Supervision](https://mlsanity.com/paper/1701.01619/) (2017)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Robustness of classifiers: from adversarial to random noise](https://mlsanity.com/paper/1608.08967/) (2016)
- [Noisy Activation Functions](https://mlsanity.com/paper/1603.00391/) (2016)
- [Spatial Deep Learning for Wireless Scheduling](https://mlsanity.com/paper/1808.01486/) (2018)
- [Analyzing noise in autoencoders and deep networks](https://mlsanity.com/paper/1406.1831/) (2014)
- [Towards Understanding the Importance of Noise in Training Neural Networks](https://mlsanity.com/paper/1909.03172/) (2019)
- [Learning Robust Beamforming for MISO Downlink Systems](https://mlsanity.com/paper/2103.01602/) (2021)
- [Resource Allocation Under Channel Uncertainties for Relay-Aided Device-to-Device Communication Underlaying LTE-A Cellular Networks](https://mlsanity.com/paper/1401.6683/) (2014)
- [Scalable Spectrum Allocation and User Association in Networks with Many Small Cells](https://mlsanity.com/paper/1701.03247/) (2017)

## Built on by (most cited first, 5 of 5)

- [Robust Communication and Computation using Deep Learning via Joint Uncertainty Injection](https://mlsanity.com/paper/2406.03548/) (2024)
- [Deep Unfolded Fractional Optimization for Maximizing Robust Throughput in 6G Networks](https://mlsanity.com/paper/2602.06062/) (2026)
- [Agentic AI-Based Joint Computing and Networking via Mixture of Experts and Large Language Models](https://mlsanity.com/paper/2605.02911/) (2026)
- [A Deep Learning Based Resource Allocator for Communication Networks with Dynamic User Utility Demands](https://mlsanity.com/paper/2311.04600/) (2023)
- [Optimizing Reinforcement Learning Training over Digital Twin Enabled Multi-fidelity Networks](https://mlsanity.com/paper/2603.08931/) (2026)

## Abstract (arXiv)

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.