# Reinforcement learning for adaptive interior point methods in convex quadratic programming

arXiv: https://arxiv.org/abs/2509.07404 · HTML: https://mlsanity.com/paper/2509.07404/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 9 Sep 2025.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 14 of 14)

- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Acceleration Methods](https://mlsanity.com/paper/2101.09545/) (2021)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [End-to-End Learning to Warm-Start for Real-Time Quadratic Optimization](https://mlsanity.com/paper/2212.08260/) (2022)
- [TFPnP: Tuning-free Plug-and-Play Proximal Algorithm with Applications to Inverse Imaging Problems](https://mlsanity.com/paper/2012.05703/) (2020)
- [PEPit: computer-assisted worst-case analyses of first-order optimization methods in Python](https://mlsanity.com/paper/2201.04040/) (2022)
- [PIQP: A Proximal Interior-Point Quadratic Programming Solver](https://mlsanity.com/paper/2304.00290/) (2023)
- [FBstab: A Stabilized Semismooth Quadratic Programming Algorithm with Applications in Model Predictive Control](https://mlsanity.com/paper/1901.04046/) (2019)
- [QPALM: A Proximal Augmented Lagrangian Method for Nonconvex Quadratic Programs](https://mlsanity.com/paper/2010.02653/) (2020)
- [An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming](https://mlsanity.com/paper/1904.10369/) (2019)
- [From Learning to Optimize to Learning Optimization Algorithms](https://mlsanity.com/paper/2405.18222/) (2024)
- [Regularized Interior Point Methods for Constrained Optimization and Control](https://mlsanity.com/paper/2210.15825/) (2022)

## Abstract (arXiv)

Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow tail-convergence typical of first-order schemes, thus requiring many iterations to achieve high-accuracy solutions. Moreover, hyperparameter tuning significantly impacts the solver performance but how to find an appropriate parameter configuration remains an elusive research question. To address these issues, we explore how data-driven approaches can accelerate the solution process. Aiming at high-accuracy solutions, we focus on a regularized interior-point solver and carefully handle its two-loop flow and control parameters. We will show that reinforcement learning can make a significant contribution to facilitating the solver tuning and to speeding up the optimization process. Numerical experiments demonstrate that, after a lightweight training, the learned policy generalizes well to different problem classes with varying dimensions.