# Learning-Assisted Algorithm Unrolling for Online Optimization with Budget Constraints

arXiv: https://arxiv.org/abs/2212.01689 · HTML: https://mlsanity.com/paper/2212.01689/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 60 references that are in the map.
- First posted on arXiv 3 Dec 2022.

## Builds on (most cited first, 23 of 23)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning](https://mlsanity.com/paper/2006.06224/) (2020)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Learned Optimizers that Scale and Generalize](https://mlsanity.com/paper/1703.04813/) (2017)
- [Serverless in the Wild: Characterizing and Optimizing the Serverless Workload at a Large Cloud Provider](https://mlsanity.com/paper/2003.03423/) (2020)
- [Dual Mirror Descent for Online Allocation Problems](https://mlsanity.com/paper/2002.10421/) (2020)
- [Fast Algorithms for Online Stochastic Convex Programming](https://mlsanity.com/paper/1410.7596/) (2014)
- [Online Primal-Dual Mirror Descent under Stochastic Constraints](https://mlsanity.com/paper/1908.00305/) (2019)
- [Online Stochastic Optimization with Wasserstein Based Non-stationarity](https://mlsanity.com/paper/2012.06961/) (2020)
- [An Algorithm Unrolling Approach to Deep Image Deblurring](https://mlsanity.com/paper/1902.05399/) (2019)
- [Deep Policies for Online Bipartite Matching: A Reinforcement Learning Approach](https://mlsanity.com/paper/2109.10380/) (2021)
- [Total Deep Variation: A Stable Regularizer for Inverse Problems](https://mlsanity.com/paper/2006.08789/) (2020)
- [Learning Aided Optimization for Energy Harvesting Devices with Outdated State Information](https://mlsanity.com/paper/1801.03572/) (2018)
- [Competitive Online Optimization under Inventory Constraints](https://mlsanity.com/paper/1901.09161/) (2019)
- [The Power of Online Learning in Stochastic Network Optimization](https://mlsanity.com/paper/1404.1592/) (2014)

## Built on by (most cited first, 1 of 1)

- [Fairness-Regularized Online Optimization with Switching Costs](https://mlsanity.com/paper/2512.11131/) (2025)

## Abstract (arXiv)

Online optimization with multiple budget constraints is challenging since the online decisions over a short time horizon are coupled together by strict inventory constraints. The existing manually-designed algorithms cannot achieve satisfactory average performance for this setting because they often need a large number of time steps for convergence and/or may violate the inventory constraints. In this paper, we propose a new machine learning (ML) assisted unrolling approach, called LAAU (Learning-Assisted Algorithm Unrolling), which unrolls the online decision pipeline and leverages an ML model for updating the Lagrangian multiplier online. For efficient training via backpropagation, we derive gradients of the decision pipeline over time. We also provide the average cost bounds for two cases when training data is available offline and collected online, respectively. Finally, we present numerical results to highlight that LAAU can outperform the existing baselines.