Learning to Optimize by Differentiable Programming: A Tutorial on Algorithm Design
A preprint tutorial on arXiv presents a framework for using differentiable programming to learn how to design first-order optimization algorithms, rather than hand-crafting them. The approach leverages modern automatic differentiation tools such as PyTorch, TensorFlow, and JAX, guided by Fenchel-Rockafellar duality to adapt iterative solvers like ADMM and PDHG. If validated, this could improve convergence and solution quality for large-scale optimization problems across engineering and machine learning applications.
A tutorial paper submitted to arXiv (cs.MS/cs.LG/math.OC) proposes a paradigm shift in optimization: instead of manually designing first-order algorithms, differentiable programming frameworks are used to learn algorithm structure end-to-end. The work leverages automatic differentiation capabilities in PyTorch, TensorFlow, and JAX to embed iterative optimization methods within trainable systems. Theoretical grounding is provided through Fenchel-Rockafellar duality, which informs the design of learnable variants of established solvers such as ADMM and PDHG. Case studies are presented across several domains, including linear programming (LP), neural network verification (NNV), sum-rate maximization, optimal power flow (OPF), and large-scale resource management problems (LRMP). The authors argue that this learned approach yields better convergence behavior and solution quality compared to fixed, hand-designed algorithms. The paper is currently in its third revision (v3, June 2026) and has not yet undergone formal peer review.
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- arXiv cs.LGCenter
Learning to Optimize by Differentiable Programming
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