![[2602.14154] A Penalty Approach for Differentiation Through Black-Box Quadratic Programming Solvers](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2602.14154] A Penalty Approach for Differentiation Through Black-Box Quadratic Programming Solvers
Summary
This paper presents dXPP, a penalty-based framework for differentiating through black-box quadratic programming solvers, improving computational efficiency and robustness over traditional KKT methods.
Why It Matters
Differentiating through quadratic programming is crucial in optimization tasks. The proposed dXPP framework addresses the limitations of existing methods, making it a significant advancement for researchers and practitioners in machine learning and optimization.
Key Takeaways
- dXPP decouples QP solving from differentiation, enhancing efficiency.
- The method is solver-agnostic, allowing flexibility in solver choice.
- Empirical results show dXPP outperforms KKT-based methods in large-scale problems.
- The approach simplifies the differentiation process, requiring only a smaller linear system.
- dXPP is applicable to various tasks, including portfolio optimization.
Computer Science > Machine Learning arXiv:2602.14154 (cs) [Submitted on 15 Feb 2026] Title:A Penalty Approach for Differentiation Through Black-Box Quadratic Programming Solvers Authors:Yuxuan Linghu, Zhiyuan Liu, Qi Deng View a PDF of the paper titled A Penalty Approach for Differentiation Through Black-Box Quadratic Programming Solvers, by Yuxuan Linghu and 2 other authors View PDF HTML (experimental) Abstract:Differentiating through the solution of a quadratic program (QP) is a central problem in differentiable optimization. Most existing approaches differentiate through the Karush--Kuhn--Tucker (KKT) system, but their computational cost and numerical robustness can degrade at scale. To address these limitations, we propose dXPP, a penalty-based differentiation framework that decouples QP solving from differentiation. In the solving step (forward pass), dXPP is solver-agnostic and can leverage any black-box QP solver. In the differentiation step (backward pass), we map the solution to a smooth approximate penalty problem and implicitly differentiate through it, requiring only the solution of a much smaller linear system in the primal variables. This approach bypasses the difficulties inherent in explicit KKT differentiation and significantly improves computational efficiency and robustness. We evaluate dXPP on various tasks, including randomly generated QPs, large-scale sparse projection problems, and a real-world multi-period portfolio optimization task. Empirical resu...
