[2601.16510] Learning to Optimize by Differentiable Programming

Computer Science > Mathematical Software arXiv:2601.16510 (cs) [Submitted on 23 Jan 2026 (v1), last revised 27 Feb 2026 (this version, v2)] Title:Learning to Optimize by Differentiable Programming Authors:Liping Tao, Xindi Tong, Chee Wei Tan View a PDF of the paper titled Learning to Optimize by Differentiable Programming, by Liping Tao and 2 other authors View PDF Abstract: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 ADMM and PDHG can be learned and adapted. Case studies across LP, OPF, Laplacian regularization, and neural network verification illustrate these gains. Subjects: Mathematical Software (cs.MS); Machine Learning (cs.LG); Optimization and Control (math.OC) Cite as: arXiv:2601.16510 [cs.MS]   (or arXiv:2601.16510v2 [cs.MS] for this version)   https://doi.org/10.48550/arXiv.2601.16510 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Liping Tao [view email] [v1] Fri, 23 Jan 202...