# Learning context-aware adaptive solvers to accelerate quadratic programming

arXiv: https://arxiv.org/abs/2211.12443 · HTML: https://mlsanity.com/paper/2211.12443/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Builds on (most cited first, 12 of 12)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Hypersolvers: Toward Fast Continuous-Depth Models](https://mlsanity.com/paper/2007.09601/) (2020)
- [ScheduleNet: Learn to solve multi-agent scheduling problems with reinforcement learning](https://mlsanity.com/paper/2106.03051/) (2021)
- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [Multi-Period Trading via Convex Optimization](https://mlsanity.com/paper/1705.00109/) (2017)
- [Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems](https://mlsanity.com/paper/1306.2454/) (2013)
- [Convergent Graph Solvers](https://mlsanity.com/paper/2106.01680/) (2021)
- [Neural Solvers for Fast and Accurate Numerical Optimal Control](https://mlsanity.com/paper/2203.08072/) (2022)
- [Implementation of model predictive control for tracking in embedded systems using a sparse extended ADMM algorithm](https://mlsanity.com/paper/2008.09071/) (2020)

## Built on by (most cited first, 7 of 7)

- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs](https://mlsanity.com/paper/2406.05938/) (2024)
- [Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process](https://mlsanity.com/paper/2401.03244/) (2024)
- [Data-Driven Performance Guarantees for Classical and Learned Optimizers](https://mlsanity.com/paper/2404.13831/) (2024)
- [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025)
- [Principled Data Augmentation for Learning to Solve Quadratic Programming Problems](https://mlsanity.com/paper/2506.01728/) (2025)
- [Data-driven Projection Generation for Efficiently Solving Heterogeneous Quadratic Programming Problems](https://mlsanity.com/paper/2510.26061/) (2025)

## Abstract (arXiv)

Convex quadratic programming (QP) is an important sub-field of mathematical optimization. The alternating direction method of multipliers (ADMM) is a successful method to solve QP. Even though ADMM shows promising results in solving various types of QP, its convergence speed is known to be highly dependent on the step-size parameter ρ. Due to the absence of a general rule for setting ρ, it is often tuned manually or heuristically. In this paper, we propose CA-ADMM (Context-aware Adaptive ADMM)) which learns to adaptively adjust ρ to accelerate ADMM. CA-ADMM extracts the spatio-temporal context, which captures the dependency of the primal and dual variables of QP and their temporal evolution during the ADMM iterations. CA-ADMM chooses ρ based on the extracted context. Through extensive numerical experiments, we validated that CA-ADMM effectively generalizes to unseen QP problems with different sizes and classes (i.e., having different QP parameter structures). Furthermore, we verified that CA-ADMM could dynamically adjust ρ considering the stage of the optimization process to accelerate the convergence speed further.