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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.02494 |
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| _version_ | 1866912742882934784 |
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| author | Zhao, Zihao Mo, Kai-Chia Ho, Shing-Hei Amos, Brandon Wang, Kai |
| author_facet | Zhao, Zihao Mo, Kai-Chia Ho, Shing-Hei Amos, Brandon Wang, Kai |
| contents | Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems. However, computing gradients via implicit differentiation requires solving a linear system with Hessian terms, which is both compute- and memory-intensive. To address this challenge, we propose a novel algorithm that computes the gradient using only first-order information. The key insight is to rewrite the differentiable optimization as a bilevel optimization problem and leverage recent advances in bilevel methods. Specifically, we introduce an active-set Lagrangian hypergradient oracle that avoids Hessian evaluations and provides finite-time, non-asymptotic approximation guarantees. We show that an approximate hypergradient can be computed using only first-order information in $\tilde{\oo}(1)$ time, leading to an overall complexity of $\tilde{\oo}(δ^{-1}ε^{-3})$ for constrained bilevel optimization, which matches the best known rate for non-smooth non-convex optimization. Furthermore, we release an open-source Python library that can be easily adapted from existing solvers. Our code is available here: https://github.com/guaguakai/FFOLayer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02494 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Fully First-Order Layer for Differentiable Optimization Zhao, Zihao Mo, Kai-Chia Ho, Shing-Hei Amos, Brandon Wang, Kai Machine Learning Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems. However, computing gradients via implicit differentiation requires solving a linear system with Hessian terms, which is both compute- and memory-intensive. To address this challenge, we propose a novel algorithm that computes the gradient using only first-order information. The key insight is to rewrite the differentiable optimization as a bilevel optimization problem and leverage recent advances in bilevel methods. Specifically, we introduce an active-set Lagrangian hypergradient oracle that avoids Hessian evaluations and provides finite-time, non-asymptotic approximation guarantees. We show that an approximate hypergradient can be computed using only first-order information in $\tilde{\oo}(1)$ time, leading to an overall complexity of $\tilde{\oo}(δ^{-1}ε^{-3})$ for constrained bilevel optimization, which matches the best known rate for non-smooth non-convex optimization. Furthermore, we release an open-source Python library that can be easily adapted from existing solvers. Our code is available here: https://github.com/guaguakai/FFOLayer. |
| title | A Fully First-Order Layer for Differentiable Optimization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2512.02494 |