# Differentiable Projection-based Learn to Optimize in Wireless Network-Part I: Convex Constrained (Non-)Convex Programming

arXiv: https://arxiv.org/abs/2502.00053 · HTML: https://mlsanity.com/paper/2502.00053/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 29 Jan 2025.

## Builds on (most cited first, 15 of 15)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Graph Neural Networks for Scalable Radio Resource Management: Architecture Design and Theoretical Analysis](https://mlsanity.com/paper/2007.07632/) (2020)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [Towards Optimal Power Control via Ensembling Deep Neural Networks](https://mlsanity.com/paper/1807.10025/) (2018)
- [Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow](https://mlsanity.com/paper/2107.00465/) (2021)
- [A General Analysis of the Convergence of ADMM](https://mlsanity.com/paper/1502.02009/) (2015)
- [A Proximal Alternating Direction Method of Multiplier for Linearly Constrained Nonconvex Minimization](https://mlsanity.com/paper/1812.10229/) (2018)
- [A Survey on Integrated Sensing, Communication, and Computation](https://mlsanity.com/paper/2408.08074/) (2024)
- [Convergence of Bregman alternating direction method with multipliers for nonconvex composite problems](https://mlsanity.com/paper/1410.8625/) (2014)

## Abstract (arXiv)

This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex optimization-based solvers often struggle to efficiently handle these problems in their most general form. While neural network (NN)-based approaches offer a promising alternative, ensuring the feasibility of NN-generated solutions and effectively training the NN remain key hurdles, largely because finite-capacity networks can produce infeasible outputs. To overcome these issues, we propose a projection-based method that projects any infeasible NN output onto the feasible domain, thus guaranteeing strict adherence to the constraints without compromising the NN's optimization capability. Furthermore, we derive the objective function values for both the raw NN outputs and their projected counterparts, along with the gradients of these values with respect to the NN parameters. This derivation enables label-free (unsupervised) training, reducing reliance on labeled data and improving scalability. Experimental results demonstrate that the proposed projection-based method consistently ensures feasibility.