# Power Control with QoS Guarantees: A Differentiable Projection-based Unsupervised Learning Framework

arXiv: https://arxiv.org/abs/2306.01787 · HTML: https://mlsanity.com/paper/2306.01787/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [Graph Neural Networks for Scalable Radio Resource Management: Architecture Design and Theoretical Analysis](https://mlsanity.com/paper/2007.07632/) (2020)
- [Convergence Rate of Frank-Wolfe for Non-Convex Objectives](https://mlsanity.com/paper/1607.00345/) (2016)
- [Learning Optimal Resource Allocations in Wireless Systems](https://mlsanity.com/paper/1807.08088/) (2018)
- [Towards Optimal Power Control via Ensembling Deep Neural Networks](https://mlsanity.com/paper/1807.10025/) (2018)
- [Wireless Power Control via Counterfactual Optimization of Graph Neural Networks](https://mlsanity.com/paper/2002.07631/) (2020)
- [Deep Unsupervised Learning for Joint Antenna Selection and Hybrid Beamforming](https://mlsanity.com/paper/2106.03127/) (2021)
- [Learning to Optimize with Unsupervised Learning: Training Deep Neural Networks for URLLC](https://mlsanity.com/paper/1905.11017/) (2019)
- [Deep Unsupervised Learning for Generalized Assignment Problems: A Case-Study of User-Association in Wireless Networks](https://mlsanity.com/paper/2103.14548/) (2021)
- [Multicell Power Control under Rate Constraints with Deep Learning](https://mlsanity.com/paper/2012.03655/) (2020)
- [Deep Learning Based Resource Assignment for Wireless Networks](https://mlsanity.com/paper/2109.12970/) (2021)

## Built on by (most cited first, 2 of 2)

- [Quantum-based QoE Optimization in Advanced Cellular Networks: Integration and Cloud Gaming Use Case](https://mlsanity.com/paper/2509.01008/) (2025)
- [Contrastive Predictive Coding with Compression for Enhanced Channel State Feedback in Wireless Networks](https://mlsanity.com/paper/2607.05419/) (2026)

## Abstract (arXiv)

Deep neural networks (DNNs) are emerging as a potential solution to solve NP-hard wireless resource allocation problems. However, in the presence of intricate constraints, e.g., users' quality-of-service (QoS) constraints, guaranteeing constraint satisfaction becomes a fundamental challenge. In this paper, we propose a novel unsupervised learning framework to solve the classical power control problem in a multi-user interference channel, where the objective is to maximize the network sumrate under users' minimum data rate or QoS requirements and power budget constraints. Utilizing a differentiable projection function, two novel deep learning (DL) solutions are pursued. The first is called Deep Implicit Projection Network (DIPNet), and the second is called Deep Explicit Projection Network (DEPNet). DIPNet utilizes a differentiable convex optimization layer to implicitly define a projection function. On the other hand, DEPNet uses an explicitly-defined projection function, which has an iterative nature and relies on a differentiable correction process. DIPNet requires convex constraints; whereas, the DEPNet does not require convexity and has a reduced computational complexity. To enhance the sum-rate performance of the proposed models even further, Frank-Wolfe algorithm (FW) has been applied to the output of the proposed models. Extensive simulations depict that the proposed DNN solutions not only improve the achievable data rate but also achieve zero constraint violation probability, compared to the existing DNNs. The proposed solutions outperform the classic optimization methods in terms of computation time complexity.