用强化学习优化二次规划求解器参数，提升精度与速度。
Reinforcement learning for adaptive interior point methods in convex quadratic programming
- 用强化学习自动调节内点法的双循环控制参数
- 轻量训练后在不同规模问题上泛化良好
- 适合需要高精度求解的优化场景
二次规划是现代非线性优化、控制和数据科学的核心工具。尽管正则化方法在最小假设下具有收敛性保证，但其收敛速度慢，常需大量迭代才能获得高精度解。此外，超参数配置显著影响求解器性能，但如何选择合适参数仍是一个难题。为此，本文探索数据驱动方法加速求解过程。针对高精度解需求，聚焦正则化内点法，细致处理其双循环流程与控制参数。实验表明，强化学习能有效提升求解器调参效率并加快优化进程。数值实验显示，经过轻量训练后，学习到的策略能在不同规模问题类别间良好泛化。
原文摘要 · Abstract (English)
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.
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