用可微编程学习优化算法，让模型自动设计更高效的求解方法。
Learning to Optimize by Differentiable Programming
- 将优化算法嵌入可微框架，通过端到端训练提升性能。
- 基于对偶理论设计迭代算法，实现收敛速度与解质量的双重优化。
- 适合对优化算法设计感兴趣的研究者与工程师参考。
求解大规模优化问题需要高效的一阶方法，且每轮计算成本低。本教程提出一种优化范式转变：不仅用可微编程执行算法，更用它来学习如何设计算法。现代框架如 PyTorch、TensorFlow 和 JAX 通过高效的自动微分支持这一范式。将一阶方法嵌入这些系统后，可实现端到端训练，从而改善收敛性与解的质量。在 Fenchel-Rockafellar 对偶理论指导下，教程展示了如何通过代表性案例，学习并调整交替方向乘子法（ADMM）和原对偶混合梯度（PDHG）等对偶启发式迭代方案。
原文摘要 · Abstract (English)
Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn how to design them. Modern frameworks such as PyTorch, TensorFlow, and JAX enable this paradigm through efficient automatic differentiation. Embedding first-order methods within these systems allows end-to-end training that improves convergence and solution quality. Guided by Fenchel-Rockafellar duality, the tutorial demonstrates how duality-informed iterative schemes such as the alternating direction method of multipliers, and the primal-dual hybrid gradient can be learned and adapted through representative case studies.
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