用神经网络学凸优化的平滑版本，让求解快十倍还准。
LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization
- 用输入凸网络学目标函数的更鲁棒版本，保持凸性与光滑性
- 实验显示比顶尖求解器快10倍，且解的质量接近最优
- 适合需要快速求解凸优化问题的研究者和工程师
我们提出LEAF，一种用于加速凸优化的学习增强型ADMM框架。核心思想是利用输入凸神经网络（ICNN）近似目标函数的Moreau包络，从而得到一个保持凸性和光滑性的可学习模型。由此衍生出MEL-ADMM及其分裂变体sMEL-ADMM。与直接学习高维算子的现有方法不同，LEAF学习的是标量值的Moreau包络，显著降低模型复杂度并提升数据效率。该框架适用于具有光滑与非光滑目标的广泛凸优化问题。通过在ICNN架构中显式嵌入凸性，所提方法在保持优化问题关键结构特性的同时，实现了高近似精度。MEL-ADMM与sMEL-ADMM均具备在学习模型下的收敛性与可行性理论保证。严格分析表明，所提方法的收敛速率与经典ADMM相当，同时降低了每轮迭代的计算成本。数值实验显示，其性能相比当前最先进求解器提升达一个数量级，且保持较小的最优性差距。
原文摘要 · Abstract (English)
We propose LEAF, a learning-enabled ADMM framework for accelerated convex optimization. The key idea is to approximate the Moreau envelope of the objective function using an Input Convex Neural Network (ICNN), resulting in a learned model that preserves convexity and smoothness. This leads to the proposed Moreau Envelope Learning ADMM (MEL-ADMM) and its splitting variant sMEL-ADMM. Unlike existing approaches that learn high-dimensional operators directly, LEAF learns a scalar-valued Moreau envelope, significantly reducing model complexity and improving data efficiency. The framework accommodates a broad class of convex problems with smooth and non-smooth objectives. By embedding convexity explicitly through the ICNN architecture, the proposed approach maintains high approximation accuracy while preserving key structural properties of the optimization problem. Both MEL-ADMM and sMEL-ADMM are developed with theoretical guarantees of convergence and feasibility under the learned model. Rigorous analysis shows that the proposed methods achieve convergence rates comparable to classical ADMM while reducing per-iteration computational cost. Numerical experiments demonstrate up to an order-of-magnitude speedup over state-of-the-art solvers while maintaining low optimality gaps
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