对偶内点优化学习
Dual Interior Point Optimization Learning
AI总结：
针对约束优化中传统求解器速度慢的问题，本文提出对偶内点优化学习方法，通过平滑自监督损失函数训练对偶线性优化代理，结合对偶补全策略保证可行性，提升求解速度且最优性间隙低于1%。
摘要：
在约束优化的许多实际应用中，规模和求解时间限制使传统优化求解器速度过慢，难以应用。因此，如何设计优化代理（即生成高质量解的机器学习模型）这一研究问题近期受到广泛关注。与聚焦学习原始解的研究方向不同，本文研究如何学习对偶可行解，以补充原始方法并提供质量保证。本文有两项独特贡献：一是针对对偶线性优化代理训练，提出平滑自监督损失函数，在目标函数中加入对偶惩罚项；二是提出新型对偶补全策略，通过求解凸优化问题保证对偶可行性，且对几类对偶惩罚项推导了补全优化的闭式解，无需计算繁重的隐式层。在大型线性优化问题上的数值结果表明，该方法有效；所提对偶补全优于未利用对偶问题结构的优化代理学习方法，与商业优化求解器相比，学习到的对偶代理最优性间隙低于1%，速度提升多个数量级。
英文摘要：
In many practical applications of constrained optimization, scale and solving time limits make traditional optimization solvers prohibitively slow. Thus, the research question of how to design optimization proxies -- machine learning models that produce high-quality solutions -- has recently received significant attention. Orthogonal to this research thread which focuses on learning primal solutions, this paper studies how to learn dual feasible solutions that complement primal approaches and provide quality guarantees. The paper makes two distinct contributions. First, to train dual linear optimization proxies, the paper proposes a smoothed self-supervised loss function that augments the objective function with a dual penalty term. Second, the paper proposes a novel dual completion strategy that guarantees dual feasibility by solving a convex optimization problem. Moreover, the paper derives closed-form solutions to this completion optimization for several classes of dual penalties, eliminating the need for computationally-heavy implicit layers. Numerical results are presented on large linear optimization problems and demonstrate the effectiveness of the proposed approach. The proposed dual completion outperforms methods for learning optimization proxies which do not exploit the structure of the dual problem. Compared to commercial optimization solvers, the learned dual proxies achieve optimality gaps below $1\%$ and several orders of magnitude speedups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
