mlsanityData to 14 Oct 2026

Safe Pontryagin Differentiable Programming

arXiv 2105.14937 ↗First posted 31 May 2021cs.LG cs.RO cs.SYcited by 26

Not on the map. Why?

Abstract (arXiv)

We propose a Safe Pontryagin Differentiable Programming (Safe PDP) methodology, which establishes a theoretical and algorithmic framework to solve a broad class of safety-critical learning and control tasks -- problems that require the guarantee of safety constraint satisfaction at any stage of the learning and control progress. In the spirit of interior-point methods, Safe PDP handles different types of system constraints on states and inputs by incorporating them into the cost or loss through barrier functions. We prove three fundamentals of the proposed Safe PDP: first, both the solution and its gradient in the backward pass can be approximated by solving their more efficient unconstrained counterparts; second, the approximation for both the solution and its gradient can be controlled for arbitrary accuracy by a barrier parameter; and third, importantly, all intermediate results throughout the approximation and optimization strictly respect the constraints, thus guaranteeing safety throughout the entire learning and control process. We demonstrate the capabilities of Safe PDP in solving various safety-critical tasks, including safe policy optimization, safe motion planning, and learning MPCs from demonstrations, on different challenging systems such as 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). Builds on 42 of its 115 references that are in the map. First posted on arXiv 31 May 2021.

Builds on

42 of 115 references.

References · 42

  1. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2015Continuous control with deep reinforcement learningcited by 3,407
  4. 2015Trust Region Policy Optimizationcited by 2,580
  5. 2017Constrained Policy Optimizationcited by 983
  6. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 599
  7. 2019Control Barrier Functions: Theory and Applicationscited by 372
  8. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 366
  9. 2015Risk-Constrained Reinforcement Learning with Percentile Risk Criteriacited by 337
  10. 2018A Lyapunov-based Approach to Safe Reinforcement Learningcited by 297
  11. 2019End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Taskscited by 289
  12. 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 287
30 more
  1. 2020Projection-Based Constrained Policy Optimizationcited by 203
  2. 2017Hamilton-Jacobi Reachability: A Brief Overview and Recent Advancescited by 201
  3. 2018Differentiable MPC for End-to-end Planning and Controlcited by 189
  4. 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 163
  5. 2019Lyapunov-based Safe Policy Optimization for Continuous Controlcited by 145
  6. 2016Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Roboticscited by 134
  7. 2019IPO: Interior-point Policy Optimization under Constraintscited by 132
  8. 2017A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applicationscited by 129
  9. 2020Safe Reinforcement Learning in Constrained Markov Decision Processescited by 115
  10. 2020Learning Control Barrier Functions from Expert Demonstrationscited by 92
  11. 2016Safe Exploration in Finite Markov Decision Processes with Gaussian Processescited by 75
  12. 2017OptLayer - Practical Constrained Optimization for Deep Reinforcement Learning in the Real Worldcited by 70
  13. 2020Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functionscited by 68
  14. 2019Convergent Policy Optimization for Safe Reinforcement Learningcited by 57
  15. 2019Pontryagin Differentiable Programming: An End-to-End Learning and Control Frameworkcited by 52
  16. 2020Enforcing robust control guarantees within neural network policiescited by 40
  17. 2021State Augmented Constrained Reinforcement Learning: Overcoming the Limitations of Learning with Rewardscited by 40
  18. 2020Neural Certificates for Safe Control Policiescited by 35
  19. 2021Enforcing Policy Feasibility Constraints through Differentiable Projection for Energy Optimizationcited by 31
  20. 2018Linear Convergence of the Primal-Dual Gradient Method for Convex-Concave Saddle Point Problems without Strong Convexitycited by 29
  21. 2017FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planningcited by 23
  22. 2021Learning Robust Hybrid Control Barrier Functions for Uncertain Systemscited by 14
  23. 2020Learning from Sparse Demonstrationscited by 9
  24. 2015Relaxed Logarithmic Barrier Function Based Model Predictive Control of Linear Systemscited by 8
  25. 2019Safe non-smooth black-box optimization with application to policy searchcited by 6
  26. 2014Safe Sequential Path Planning of Multi-Vehicle Systems via Double-Obstacle Hamilton-Jacobi-Isaacs Variational Inequalitycited by 4
  27. 2018Inverse Optimal Control from Incomplete Trajectory Observationscited by 4
  28. 2020Interior Point Differential Dynamic Programmingcited by 4
  29. 2017A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systemscited by 2
  30. 2020Equality Constrained Linear Optimal Control With Factor Graphscited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 7; 2023: 4; 2024: 4; 2025: 5; 2026: 5.

26 papers.

Sort:

By area:

  1. 2022Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environmentscited by 60
  2. 2022Joint Differentiable Optimization and Verification for Certified Reinforcement Learningcited by 11
  3. 2022Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environmentscited by 9
  4. 2023Revisiting Implicit Differentiation for Learning Problems in Optimal Controlcited by 8
  5. 2023Constrained Meta-Reinforcement Learning for Adaptable Safety Guarantee with Differentiable Convex Programmingcited by 8
  6. 2022Provable Safe Reinforcement Learning with Binary Feedbackcited by 7
  7. 2024DiffTORI: Differentiable Trajectory Optimization for Deep Reinforcement and Imitation Learningcited by 6
  8. 2022Neural Moving Horizon Estimation for Robust Flight Controlcited by 5
  9. 2024Online Control-Informed Learningcited by 4
  10. 2021Learning Linear Complementarity Systemscited by 3
  11. 2025End-to-End Training of High-Dimensional Optimal Control with Implicit Hamiltonians via Jacobian-Free Backpropagationcited by 3
  12. 2024A Differential Dynamic Programming Framework for Inverse Reinforcement Learningcited by 2
14 more
  1. 2025DiffCoord: Differentiable Coordination for Distributed Multi-Agent Trajectory Optimizationcited by 2
  2. 2022Optimisation of Structured Neural Controller Based on Continuous-Time Policy Gradientcited by 1
  3. 2022Distributed Differentiable Dynamic Game for Multi-robot Coordinationcited by 1
  4. 2023Distributionally Safe Reinforcement Learning under Model Uncertainty: A Single-Level Approach by Differentiable Convex Programmingcited by 1
  5. 2024Shadow Program Inversion with Differentiable Planning: A Framework for Unified Robot Program Parameter and Trajectory Optimizationcited by 1
  6. 2025Learning Agile Gate Traversal via Analytical Optimal Policy Gradientcited by 1
  7. 2025Safe Online Control-Informed Learningcited by 1
  8. 2026On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonianscited by 1
  9. 2023Adaptive Policy Learning to Additional Taskscited by 0
  10. 2025Model-free Reinforcement Learning for Model-based Control: Towards Safe, Interpretable and Sample-efficient Agentscited by 0
  11. 2026Deep-Unfolded Coordinationcited by 0
  12. 2026Safe Online Learning via Smooth Safety-Structured Policy Compositioncited by 0
  13. 2026End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layerscited by 0
  14. 2026lapanda: A Matrix-Free Differentiable Solver for Nonconvex Constrained Optimization Layerscited by 0