Differentiable Optimization

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Differentiable optimization studies how to compute gradients through iterative algorithms and constrained decisions so their parameters or inputs can be learned end to end. Common approaches unroll solver iterations, use implicit differentiation or adjoints, or build differentiable layers from projections, quadratic programs, and conic solvers. These methods support tasks such as hyperparameter tuning, decision-focused prediction, robotics control, and physics-based design, where improving the final decision matters as much as improving a prediction. A central challenge is balancing scalable, reliable gradients with exact feasibility and discrete or nonsmooth decisions, especially in large or numerically sensitive problems.

Latest papers

84 papers10 papers in the last four weeks, up 25% on the four weeks before. 0.1% of all new papers.

Decision-Focused Learning via Tangent-Space Projection of Prediction Error
May 2, 2026Junhyeong Lee, Sangjin Jin, Yongjae LeeDecision-Focused Learning Differentiable Optimization
Department of Industrial Engineering, Ulsan National Institute of Science and Technology, Ulsan, South Korea.
Differentiable Multiphysics Co-Optimization via Implicit Neural Representations: A Transient Hamburger-Cooking Benchmark
May 1, 2026Navid ZobeiryDifferentiable Optimization Multi-Objective Optimization
Department of Materials Science and Engineering, University of Washington · William E. Boeing Department of Aeronautics & Astronautics, University of Washington, Seattle, WA 98195, USA
NLPOpt-Net: A Learning Method for Nonlinear Optimization with Feasibility Guarantees
Apr 30, 2026Bimol Nath Roy, Rahul Golder, MM Faruque HasanNeural Network Optimization Learning to Optimize
Texas A&M University
Differentiable Satellite Constellation Configuration via Relaxed Coverage and Revisit Objectives
Apr 21, 2026Shreeyam Kacker, Kerri CahoyDifferentiable Programming Differentiable Optimization
Department of Aeronautics and Astronautics MIT
VertAX: a differentiable vertex model for learning epithelial tissue mechanics
Apr 8, 2026Alessandro Pasqui, Jim Martin Catacora Ocana, Anshuman Sinha +7Differentiable Physics Differentiable Optimization
Center for Interdisciplinary Research in Biology (CIRB), Collège de France, Université PSL, CNRS, INSERM, 75005 Paris, France. · Current address: Center for Integrative Biology (CBI), University of Toulouse, CNRS, Toulouse, France. · Center for Life Nano & Neuro Science, IIT, 00161, Rome, Italy. +3
LMI-Net: Linear Matrix Inequality--Constrained Neural Networks via Differentiable Projection Layers
Apr 7, 2026Sunbochen Tang, Andrea Goertzen, Navid AzizanConstrained Optimization Differentiable Optimization
Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Differentiable Stroke Planning with Dual Parameterization for Efficient and High-Fidelity Painting Creation
Apr 3, 2026Jinfan Liu, Wuze Zhang, Zhangli Hu +3Differentiable Rendering Differentiable Optimization
Shanghai Jiao Tong University
Differentiable SpaTiaL: Symbolic Learning and Reasoning with Geometric Temporal Logic for Manipulation Tasks
Apr 3, 2026Licheng Luo, Kaier Liang, Cristian-Ioan Vasile +1Differentiable Logic Spatiotemporal Reasoning
UC Riverside · Lehigh University
Efficient Bilevel Optimization with KFAC-Based Hypergradients
Mar 31, 2026Disen Liao, Felix Dangel, Yaoliang YuKronecker-Factored Approximation Bilevel Optimization
University of Waterloo · Vector Institute
Differentiable Initialization-Accelerated CPU-GPU Hybrid Combinatorial Scheduling
Mar 30, 2026Mingju Liu, Jiaqi Yin, Alvaro Velasquez +1Combinatorial Optimization Integer Linear Programming
University of Maryland, College Park, Maryland, USA · University of Colorado, Boulder, Colorado, USA
MetaTune: Adjoint-based Meta-tuning via Robotic Differentiable Dynamics
Mar 28, 2026Xiexin Peng, Bingheng Wang, Tao Zhang +2Robust Control Feedback Control
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China · Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore · Wuhan Zhenyou Technology Co., Ltd., Wuhan 430205, China
Sample-Efficient Hypergradient Estimation for Decentralized Bi-Level Reinforcement Learning
Mar 16, 2026Mikoto Kudo, Takumi Tanabe, Akifumi Wachi +1Hypergradient Optimization Decentralized MARL
University of Tsukuba · RIKEN AIP · LY Corporation
FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems
Mar 2, 2026Minwoo Kim, Seunghyeok Shin, Hongki LimDiffusion-Based Inverse Problems Inverse Problems
Department of Electrical and Computer Engineering, Inha University Incheon, 22212, South Korea
End-to-end Differentiable Calibration and Reconstruction for Optical Particle Detectors
Feb 27, 2026Omar Alterkait, César Jesús-Valls, Ryo Matsumoto +2Differentiable Physics Differentiable Optimization
Department of Physics and Astronomy, Tufts University, 574 Boston Ave, Medford, MA 02155, USA · The NSF AI Institute for Fundamental Interactions, MIT, Cambridge, MA 02139, USA · European Organization for Nuclear Research (CERN), 1211 Geneva 23, Switzerland +3
Differentiable Zero-One Loss via Hypersimplex Projections
Feb 26, 2026Camilo Gomez, Pengyang Wang, Liansheng TangClassification Deep Learning Optimization
School of Data, Mathematical, and Statistical Sciences, University of Central Florida, Orlando, USA · Department of CIS, University of Macau, Macao, China
GauS: Differentiable Scheduling Optimization via Gaussian Reparameterization
Feb 23, 2026Yaohui Cai, Vesal Bakhtazad, Cunxi Yu +1Differentiable Optimization
Cornell University · University of Maryland, College Park
Understanding the Curse of Unrolling
Feb 23, 2026Sheheryar Mehmood, Florian Knoll, Peter OchsAlgorithm Unrolling Differentiable Optimization
Saarland University, Saarbrücken, Germany · Friedrich-Alexander University, Erlangen, Germany
Understanding the Generalization of Bilevel Programming in Hyperparameter Optimization: A Tale of Bias-Variance Decomposition
Feb 20, 2026Yubo Zhou, Jun Shu, Junmin Liu +1Hypergradient Optimization Hyperparameter Optimization
School of Mathematics and Statistics and Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an, 100190, Shaan’xi Province, P. R. China. · Pazhou Lab (Huangpu), Street, Guangzhou, Guangdong Province, P. R. China.
RoboLayout: Differentiable 3D Scene Generation for Embodied Agents
Feb 18, 2026Ali Shamsaddinlou3D Scene Layout Generation 3D Scene Generation
Shiva-DiT: Residual-Based Differentiable Top- $k$ Selection for Efficient Diffusion Transformers
Feb 5, 2026Jiaji Zhang, Hailiang Zhao, Jiaju Wu +3Diffusion Model Acceleration Diffusion Transformer
College of Computer Science and Technology, Zhejiang University · 3Nanyang Technological University
Learning to Optimize by Differentiable Programming
Jan 23, 2026Liping Tao, Xindi Tong, Chee Wei TanPrimal-Dual Optimization Learning to Optimize
Nanyang Technological University, Singapore · Nanyang Technological University, Singapore, Singapore
Learning to bin: differentiable and Bayesian optimization for multi-dimensional discriminants in high-energy physics
Jan 12, 2026Johannes Erdmann, Nitish Kumar Kasaraguppe, Florian MausolfHigh-Energy Physics Differentiable Optimization
RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transport
Sep 2, 2025Samuel Boïté, Eloi Tanguy, Julie Delon +2Gaussian Mixture Models Expectation-Maximization
Université Paris Cité, CNRS, MAP5, F-75006 Paris, France · Centre Borelli, CNRS and ENS Paris-Saclay, F-91190 Gif-sur-Yvette, France · CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris
Accelerating Optimization via Differentiable Stopping Time
May 28, 2025Zhonglin Xie, Yiman Fong, Haoran Yuan +1Differentiable Optimization Hyperparameter Optimization
Beijing International Center for Mathematical Research, Peking University · Department of Industrial Engineering, Tsinghua University · School of Mathematics Science, Peking University

May 2, 2026J/K move · Enter open · S save

Decision-Focused Learning via Tangent-Space Projection of Prediction Error

Junhyeong Lee, Sangjin Jin, Yongjae Lee

Department of Industrial Engineering, Ulsan National Institute of Science and Technology, Ulsan, South Korea.

Decision-Focused Learning Differentiable Optimization

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Decision-Focused Learning (DFL) trains predictors to improve downstream decision quality, but computing regret gradients typically requires differentiating through solvers or relying on surrogate losses, which can be computationally expensive or deviate from the true objective. We show that, under standard regularity with locally stable active constraints, the regret gradient admits a closed-form geometric characterization, equivalent to the prediction error projected onto the tangent space of active constraints, scaled by local curvature. This reveals that regret gradients can be obtained by filtering decision-irrelevant components from the MSE gradient, providing a simpler and more direct alternative to existing approaches. Based on this, we propose PEAR (Projected Error As Regret-gradient), which computes regret gradients via a reduced linear system over active constraints, avoiding differentiation through solver iterations or additional optimization solves. Experiments on LP benchmarks and a real-world QP task show that PEAR achieves the best decision quality among all baselines while being the most computationally efficient, with gains that persist under constraint shifts.