mlsanityData to 7 Oct 2026

Differentiating Through a Cone Program

arXiv 1904.09043 ↗First posted 19 Apr 2019math.OCcited by 72

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Abstract (arXiv)

We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its homogeneous self-dual embedding, and solving the linear systems of equations required using an iterative method. This allows us to efficiently compute the derivative operator, and its adjoint, evaluated at a vector. These correspond to computing an approximate new solution, given a perturbation to the cone program coefficients (i.e., perturbation analysis), and to computing the gradient of a function of the solution with respect to the coefficients. Our method scales to large problems, with numbers of coefficients in the millions. We present an open-source Python implementation of our method that solves a cone program and returns the derivative and its adjoint as abstract linear maps; our implementation can be easily integrated into software systems for automatic differentiation.

Key facts. Cited by 72 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Apr 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 12; 2022: 9; 2023: 19; 2024: 13; 2025: 8; 2026: 11.

72 papers.

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  1. 2021Efficient and Modular Implicit Differentiationcited by 199
  2. 2023Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunitiescited by 129
  3. 2021Strategic Classification Made Practicalcited by 58
  4. 2021CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraintscited by 49
  5. 2021Nonsmooth Implicit Differentiation for Machine Learning and Optimizationcited by 43
  6. 2022PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programmingcited by 32
  7. 2023RAYEN: Imposition of Hard Convex Constraints on Neural Networkscited by 30
  8. 2022Backpropagation through Combinatorial Algorithms: Identity with Projection Workscited by 29
  9. 2021Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networkscited by 26
  10. 2022Alternating Differentiation for Optimization Layerscited by 22
  11. 2022SurCo: Learning Linear Surrogates For Combinatorial Nonlinear Optimization Problemscited by 21
  12. 2021Efficient differentiable quadratic programming layers: an ADMM approachcited by 19
38 more
  1. 2025FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guaranteescited by 19
  2. 2022Flexible Differentiable Optimization via Model Transformationscited by 16
  3. 2021The Perils of Learning Before Optimizingcited by 15
  4. 2023Backpropagation of Unrolled Solvers with Folded Optimizationcited by 13
  5. 2021Deep Learning Explicit Differentiable Predictive Control Laws for Buildingscited by 11
  6. 2023Differentiating Through Integer Linear Programs with Quadratic Regularization and Davis-Yin Splittingcited by 11
  7. 2024Dual Lagrangian Learning for Conic Optimizationcited by 11
  8. 2025Conformal Risk Training: End-to-End Optimization of Conformal Risk Controlcited by 11
  9. 2023Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learningcited by 10
  10. 2024Differentiation Through Black-Box Quadratic Programming Solverscited by 10
  11. 2024BPQP: A Differentiable Convex Optimization Framework for Efficient End-to-End Learningcited by 10
  12. 2023Benchmarking PtO and PnO Methods in the Predictive Combinatorial Optimization Regimecited by 8
  13. 2024Differentiable Distributionally Robust Optimization Layerscited by 8
  14. 2021Diff-Explainer: Differentiable Convex Optimization for Explainable Multi-hop Inferencecited by 7
  15. 2021Differentiable Rendering with Perturbed Optimizerscited by 7
  16. 2023End-to-End Reinforcement Learning of Koopman Models for Economic Nonlinear Model Predictive Controlcited by 6
  17. 2023The Pursuit of Human Labeling: A New Perspective on Unsupervised Learningcited by 6
  18. 2024DataSP: A Differential All-to-All Shortest Path Algorithm for Learning Costs and Predicting Paths with Contextcited by 6
  19. 2024LPGD: A General Framework for Backpropagation through Embedded Optimization Layerscited by 6
  20. 2023Deep Declarative Dynamic Time Warping for End-to-End Learning of Alignment Pathscited by 5
  21. 2023SCQPTH: an efficient differentiable splitting method for convex quadratic programmingcited by 5
  22. 2022On the complexity of nonsmooth automatic differentiationcited by 4
  23. 2022Learning Sparsity-Promoting Regularizers using Bilevel Optimizationcited by 4
  24. 2023Predict-Then-Optimize by Proxy: Learning Joint Models of Prediction and Optimizationcited by 4
  25. 2021DeepPSL: End-to-end perception and reasoningcited by 3
  26. 2021Bilevel learning of l1-regularizers with closed-form gradients(BLORC)cited by 3
  27. 2023Data-driven and Physics Informed Modelling of Chinese Hamster Ovary Cell Bioreactorscited by 3
  28. 2023On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approachcited by 3
  29. 2023Differentiable Cutting-plane Layers for Mixed-integer Linear Optimizationcited by 3
  30. 2024Learning Joint Models of Prediction and Optimizationcited by 3
  31. 2025A Fully First-Order Layer for Differentiable Optimizationcited by 3
  32. 2026Decision-Focused Learning via Tangent-Space Projection of Prediction Errorcited by 3
  33. 2023Implicit Bilevel Optimization: Differentiating through Bilevel Optimization Programmingcited by 2
  34. 2023Wasserstein Distributionally Robust Control Barrier Function using Conditional Value-at-Risk with Differentiable Convex Programmingcited by 2
  35. 2024End-to-End Learning for Fair Multiobjective Optimization Under Uncertaintycited by 2
  36. 2024Decision-Focused Forecasting: A Differentiable Multistage Optimisation Architecturecited by 2
  37. 2024Differentiable Convex Optimization Layers in Neural Architectures: Foundations and Perspectivescited by 2
  38. 2026A Penalty Approach for Differentiation Through Black-Box Quadratic Programming Solverscited by 2

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