# Learning to Optimize Under Constraints with Unsupervised Deep Neural Networks

arXiv: https://arxiv.org/abs/2101.00744 · HTML: https://mlsanity.com/paper/2101.00744/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 4 Jan 2021.

## Builds on (most cited first, 5 of 5)

- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization](https://mlsanity.com/paper/2006.01610/) (2020)
- [Spatial Deep Learning for Wireless Scheduling](https://mlsanity.com/paper/1808.01486/) (2018)

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

- [Deep Learning for Modeling and Dispatching Hybrid Wind Farm Power Generation](https://mlsanity.com/paper/2512.00728/) (2025)
- [A Constraint-Aware Generative Framework for Synthetic Origin-Destination Demand in Logistics Networks](https://mlsanity.com/paper/2609.04345/) (2026)

## Abstract (arXiv)

In this paper, we propose a machine learning (ML) method to learn how to solve a generic constrained continuous optimization problem. To the best of our knowledge, the generic methods that learn to optimize, focus on unconstrained optimization problems and those dealing with constrained problems are not easy-to-generalize. This approach is quite useful in optimization tasks where the problem's parameters constantly change and require resolving the optimization task per parameter update. In such problems, the computational complexity of optimization algorithms such as gradient descent or interior point method preclude near-optimal designs in real-time applications. In this paper, we propose an unsupervised deep learning (DL) solution for solving constrained optimization problems in real-time by relegating the main computation load to offline training phase. This paper's main contribution is proposing a method for enforcing the equality and inequality constraints to the DL-generated solutions for generic optimization tasks.