# Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management

arXiv: https://arxiv.org/abs/1705.09412 · HTML: https://mlsanity.com/paper/1705.09412/

## Key facts

- Cited by 96 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2017.

## Built on by (most cited first, 30 of 96)

- [Edge Artificial Intelligence for 6G: Vision, Enabling Technologies, and Applications](https://mlsanity.com/paper/2111.12444/) (2021)
- [Graph Neural Networks for Wireless Communications: From Theory to Practice](https://mlsanity.com/paper/2203.10800/) (2022)
- [An Introduction to Bi-level Optimization: Foundations and Applications in Signal Processing and Machine Learning](https://mlsanity.com/paper/2308.00788/) (2023)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Decentralized Inference with Graph Neural Networks in Wireless Communication Systems](https://mlsanity.com/paper/2104.09027/) (2021)
- [B2Opt: Learning to Optimize Black-box Optimization with Little Budget](https://mlsanity.com/paper/2304.11787/) (2023)
- [Scalable Power Control/Beamforming in Heterogeneous Wireless Networks with Graph Neural Networks](https://mlsanity.com/paper/2104.05463/) (2021)
- [Holistic Network Virtualization and Pervasive Network Intelligence for 6G](https://mlsanity.com/paper/2301.00519/) (2023)
- [Modular Meta-Learning for Power Control via Random Edge Graph Neural Networks](https://mlsanity.com/paper/2108.13178/) (2021)
- [Learning to Continuously Optimize Wireless Resource in a Dynamic Environment: A Bilevel Optimization Perspective](https://mlsanity.com/paper/2105.01696/) (2021)
- [Federated Learning and Meta Learning: Approaches, Applications, and Directions](https://mlsanity.com/paper/2210.13111/) (2022)
- [A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimization](https://mlsanity.com/paper/2207.05364/) (2022)
- [Joint Deep Reinforcement Learning and Unfolding: Beam Selection and Precoding for mmWave Multiuser MIMO with Lens Arrays](https://mlsanity.com/paper/2101.01336/) (2021)
- [Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems](https://mlsanity.com/paper/2112.08091/) (2021)
- [Deep Graph Unfolding for Beamforming in MU-MIMO Interference Networks](https://mlsanity.com/paper/2304.00446/) (2023)
- [Learning Robust Beamforming for MISO Downlink Systems](https://mlsanity.com/paper/2103.01602/) (2021)
- [Algorithm Unrolling for Massive Access via Deep Neural Network with Theoretical Guarantee](https://mlsanity.com/paper/2106.10426/) (2021)
- [Graph-based Algorithm Unfolding for Energy-aware Power Allocation in Wireless Networks](https://mlsanity.com/paper/2201.11799/) (2022)
- [Privacy-Preserving Decentralized Inference with Graph Neural Networks in Wireless Networks](https://mlsanity.com/paper/2208.06963/) (2022)
- [ENGNN: A General Edge-Update Empowered GNN Architecture for Radio Resource Management in Wireless Networks](https://mlsanity.com/paper/2301.00757/) (2022)
- [Uncertainty Injection: A Deep Learning Method for Robust Optimization](https://mlsanity.com/paper/2302.12304/) (2023)
- [Graph Neural Networks for Power Allocation in Wireless Networks with Full Duplex Nodes](https://mlsanity.com/paper/2303.16113/) (2023)
- [Two-Stage Stochastic Optimization via Primal-Dual Decomposition and Deep Unrolling](https://mlsanity.com/paper/2105.01853/) (2021)
- [Learn to Communicate with Neural Calibration: Scalability and Generalization](https://mlsanity.com/paper/2110.00272/) (2021)
- [Differentiable Projection for Constrained Deep Learning](https://mlsanity.com/paper/2111.10785/) (2021)
- [Learning for Robust Combinatorial Optimization: Algorithm and Application](https://mlsanity.com/paper/2112.10377/) (2021)
- [MR-iNet Gym: Framework for Edge Deployment of Deep Reinforcement Learning on Embedded Software Defined Radio](https://mlsanity.com/paper/2204.04507/) (2022)
- [Data-driven decision-focused surrogate modeling](https://mlsanity.com/paper/2308.12161/) (2023)
- [Deep Learning Based Uplink Multi-User SIMO Beamforming Design](https://mlsanity.com/paper/2309.16603/) (2023)
- [Deep Joint Semantic Coding and Beamforming for Near-Space Airship-Borne Massive MIMO Network](https://mlsanity.com/paper/2405.19889/) (2024)

## Abstract (arXiv)

For the past couple of decades, numerical optimization has played a central role in addressing wireless resource management problems such as power control and beamformer design. However, optimization algorithms often entail considerable complexity, which creates a serious gap between theoretical design/analysis and real-time processing. To address this challenge, we propose a new learning-based approach. The key idea is to treat the input and output of a resource allocation algorithm as an unknown non-linear mapping and use a deep neural network (DNN) to approximate it. If the non-linear mapping can be learned accurately by a DNN of moderate size, then resource allocation can be done in almost real time -- since passing the input through a DNN only requires a small number of simple operations. In this work, we address both the thereotical and practical aspects of DNN-based algorithm approximation with applications to wireless resource management. We first pin down a class of optimization algorithms that are `learnable' in theory by a fully connected DNN. Then, we focus on DNN-based approximation to a popular power allocation algorithm named WMMSE (Shi it et al 2011). We show that using a DNN to approximate WMMSE can be fairly accurate -- the approximation error ε depends mildly [in the order of log(1/ε)] on the numbers of neurons and layers of the DNN. On the implementation side, we use extensive numerical simulations to demonstrate that DNNs can achieve orders of magnitude speedup in computational time compared to state-of-the-art power allocation algorithms based on optimization.