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.

Sparse Sum-of-Squares Layers for Certified Learning
Oct 25, 2026Ege Gursoy, Nicolas MansardSemidefinite Programming Differentiable Optimization
LAAS-CNRS · ANITI
A Tutorial on Physics Constrained Machine Learning for Hybrid Modeling, Optimization, and Control
Oct 23, 2026Rahul Golder, Bimol Nath Roy, MM Faruque HasanPhysics-Informed ML Differentiable Optimization
Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77843-3122, USA · Texas A&M Energy Institute, Texas A&M University, College Station, TX 77843, USA
End-to-End Differentiable Diffusion Conditioning for Physics-Informed Optimization
Oct 22, 2026Ricardo Luna Gutierrez, Vineet Gundecha, Rahman Ejaz +5Differentiable Optimization
Hewlett Packard Enterprise · University of Rochester
Self-Supervised Tuning of Low-Fidelity Optimization Models via High-Fidelity Feedback
Oct 20, 2026Gonzalo E. Constante-Flores, André H. Quisaguano-Paredes, Asha Ramanujam +2Learning to Optimize Multi-Fidelity Optimization
Department of Electrical, Computer & Energy Engineering, University of Colorado Boulder · Davidson School of Chemical Engineering, Purdue University · ExxonMobil Technology and Engineering Company
VBO-MI: A Differentiable Black-Box Optimization Framework via Variational Mutual Information Estimation
Oct 17, 2026Farhad MirkarimiBayesian Optimization Black-Box Optimization
McGill University
Decision-Focused Learning in MDPs: An Occupancy Measure Approach
Oct 6, 2026Zihao Zhao, Ashwath K. Karunakaram, Ali Eshragh +2Markov Decision Processes Decision-Focused Learning
Georgia Institute of Technology, Atlanta, GA · Johns Hopkins Carey Business School, Washington, DC · International Computer Science Institute, Berkeley, CA
Trinity: One Differentiable Physics for Training, Refining and Scoring Generative Floorplanners
Oct 4, 2026Shih-Ying Yeh, Tzu-Sian Wang, Xuehai Wang +7Floor Plan Generation Electronic Design Automation
National Tsing Hua University · Kohaku Lab · Karolinska Institutet +2
Autoregressive Differentiable Method for Integer Programming
Oct 1, 2026Ouns El Harzli, Yudong CaoCombinatorial Optimization Neural Combinatorial Optimization
BCG X AI Science Institute Boston, USA · Zapata Quantum Boston, USA
Same Loss, Different Gradients
Sep 30, 2026Ningkang Peng, Xiaoqian Peng, Yifan He +4Automatic Differentiation Differentiable Optimization
Nanjing Normal University · Nanjing University of Chinese Medicine
On the Numerical Reliability of Differentiable Physics-Based Optimization for Robotic Material Manipulation
Sep 28, 2026Xintong Yang, Minglun Wei, Yu-Kun Lai +1Robot Dynamics Identification Material Point Method
School of Engineering, Cardiff University, Cardiff, United Kingdom · School of Computer Science and Informatics, Cardiff University, Cardiff, United Kingdom · College of Mechanical and Electrical Engineering, Hohai University, China
dOPT: Differentiating Conic Optimization via Geometric Reduction
Sep 27, 2026Fengyu Yang, Connor W. Magoon, Tyler Watts +1Implicit Differentiation Differentiable Programming
Department of Mathematics University of North Carolina at Chapel Hill
lapanda: A Matrix-Free Differentiable Solver for Nonconvex Constrained Optimization Layers
Sep 27, 2026Yuankun Chen, Zifei Nie, Kangyu Lin +2Differentiable Programming Nonconvex Optimization
School of Artificial Intelligence, Jilin University, China · Graduate School of Informatics, Kyoto University, JPN · Department of Civil and Systems Engineering, Johns Hopkins University, USA
Bilevel Optimization of Topology and Hyperparameters (BOTH)
Sep 18, 2026Suryanarayanan Manoj Sanu, Miguel Anibal Bessa, Alejandro Marcos AragónHypergradient Optimization Topology Optimization
Faculty of Mechanical Engineering Delft university of technology Delft The Netherlands · School of engineering Brown University Providence United States of America
Customizable and Jointly Optimized Route Planning: A Deep Architecture Enabling Differentiable Shortest-Path Search
Sep 17, 2026Rui Zhao, Chao Chen, Longfei Xu +4Graph-Based Planning Differentiable Optimization
Alibaba Group Beijing, China · Alibaba Group Hangzhou, China
HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimization
Sep 14, 2026Kangzheng Liu, Uday Kumar Punna, Leixin MaTopology Optimization Structural Mechanics
School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, 85287, AZ, USA
Benchmarking Optimizers to Solve Inverse Problems with Differentiable Physics Simulators
Sep 12, 2026Xiang Chen, Huanhuan XiaDifferentiable Optimization Inverse Problems
Zhongguancun Academy, Beijing, China · Zhongguancun Institute of Artificial Intelligence, Beijing, China
Differentiable Hybrid Modelling for Learning and Optimising Chemical Transport Processes from Experimental Data
Sep 3, 2026Arthur Jessop, Mohammed Alsubeihi, Ben Moseley +1Differentiable Physics Differentiable Optimization
Department of Chemical Engineering, The University of Manchester, Manchester, M13 9PL, United Kingdom. · Department of Earth Science and Engineering, Imperial College London, South Kensington, SW7 2BX, United Kingdom. · I-X Centre for AI in Science, Imperial College London, South Kensington, SW7 2BX, United Kingdom.
Differentiable Electricity-Market Clearing for Gradient-Based Planning
Sep 2, 2026Luca Mungo, Maarten P. Scholl, Arnau Quera-BofarullDifferentiable Optimization
Macrocosm Inc. · Institute for New Economic Thinking, University of Oxford
Differentiable Voxelization of Surface Representations
Aug 16, 2026Tobias Djuren, Ugo Finnendahl, Markus Worchel +23D Mesh Deformation Differentiable Optimization
Technische Universität Berlin, Germany
PPAPlace: Differentiable Cross-Stage Objectives for Chip Placement Optimization
Aug 13, 2026Ruogu Chen, Jie HanMacro Placement Electronic Design Automation
University of Alberta Department of Electrical and Computer Engineering Edmonton, AB, Canada
Hölder Signed Distance: A Differentiable, Signed, Parallelizable Metric for Robotics
Aug 7, 2026Felipe Bartelt, Ali Umut Kaypak, Anthony Tzes +3Signed Distance Functions Differentiable Optimization
Fast LapSum: Exact Differentiable Top- $k$ at Million Scale
Aug 7, 2026Jakub Antczak, Joanna Wojciechowicz, Kamil Książek +3Differentiable Programming Differentiable Optimization
Wrocław University of Science and Technology Wrocław, Poland · Centre for Credible Artificial Intelligence Warsaw University of Technology Warsaw, Poland · Jagiellonian University Kraków, Poland
Differentiating Through Dual Prices: End-to-End Policy Learning Under Capacity Constraints
Aug 5, 2026Mohammadsaeed Haghi, Mahdi Salmani, Nima Kelidari +2Constrained Optimization Differentiable Optimization
University of Southern California
Hard Constraints, Smooth Gradients: Learning Feasible Inventory Policies via Differentiable Projection
Aug 3, 2026Patrick Helm, Jan-Niklas Doerr, Joren Gijsbrechts +1Inventory Control Constrained RL
TUM School of Management, Technical University of Munich · Esade, Ramon Llull University · Munich Data Science Institute (MDSI), Technical University of Munich
Amortising Trajectory Optimisation for Residual MPC via Implicit Contact Differentiation
Jul 27, 2026Daniel Layeghi, Thomas Corbères, Calum Arnott +4Trajectory Optimization Automatic Differentiation
School of Informatics, University of Edinburgh, Scotland.
Smooth Learning with Hard Constraints via Legendre-Regularized Policies
Jul 27, 2026Zikun Lin, Rui Chen, Yijie WangDecision-Focused Learning Constrained Optimization
Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong, China. · School of Data Science, The Chinese University of Hong Kong, Shenzhen, Guangdong, China. · School of Economics and Management, Tongji University, Shanghai, China.
End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layers
Jul 22, 2026Xingjian Li, Kelvin Kan, Deepanshu Verma +3Safety-Critical Control Control Barrier Functions
UT Austin · UCLA · Clemson University +1
Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentation
Jul 8, 2026Youcheng Zong, Runda Jia, Minxuan Hu +2Image Segmentation Topology-Preserving Image Segmentation
College of Information Science and Engineering, Northeastern University, Shenyang 110004, China · Changsha Stomatological Hospital, Changsha 410005, China
Directly Optimizing Mean Demographic Parity for Nonlinear Regression
Jul 6, 2026Ieva Petrulionyte, Julien Mairal, Michael ArbelAlgorithmic Fairness Group Fairness
Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France
Smooth $\%$ MinMax: A Differentiable Relaxation for Codon Harmonization
Jul 4, 2026Yoonho Jeong, Hyunwoo Choi, Ryan Fernandez Medina Hariri +3Differentiable Optimization
Department of Chemistry, KAIST, Daejeon 34141, Korea. · School of Chemistry and Chemical Engineering, Highfield Campus, University of Southampton, Southampton SO17 1BJ, United Kingdom.

Oct 25, 2026J/K move · Enter open · S save

Sparse Sum-of-Squares Layers for Certified Learning

Ege Gursoy, Nicolas Mansard

LAAS-CNRS · ANITI

Semidefinite Programming Differentiable Optimization Neural Network Verification

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A central limitation of modern machine learning systems is the lack of formal certificates guaranteeing their behavior beyond empirical, sample-based evaluation. Sum-of-squares (SOS) methods provide such guarantees by certifying polynomial inequalities over continuous domains via semidefinite programming (SDP). While prior work has introduced SDP layers as differentiable components in neural networks, repeated learning calls can lose the computational benefit of the forward program's sparse representation. We propose Sparse SOS Layers, differentiable value layers whose backward passes reuse the local coordinates of the forward solve. Under a fixed template and learned objective coefficients, each layer avoids building dense certificates and reuses its sparse structure across training steps. Compared with existing methods, our approach achieves up to 2.7 times speedup in total warm-call time, with nearly 100 times lower memory usage (1.7 vs. 160 GiB) for relatively large problem sizes for the tested dense parameterization. Experiments cover sparse polynomial certification, pendulum control, combinatorial relaxations, robotics projection, oscillator chains, and pose graph synchronization. A design study achieves zero certified violations across unseen problem instances and sizes, while requiring roughly 7 times fewer optimization solves than estimating gradients by perturbing the objective coefficients and re-solving the problem (finite differences). These results show that sparse certificate values can be effectively integrated into learning pipelines when the backward pass respects the verifier's structure.