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Lipschitz Continuity in Model-based Reinforcement Learning

arXiv 1804.07193 ↗First posted 19 Apr 2018cs.LG cs.AI stat.MLcited by 90

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Abstract (arXiv)

We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the Wasserstein metric. We go on to prove an error bound for the value-function estimate arising from Lipschitz models and show that the estimated value function is itself Lipschitz. We conclude with empirical results that show the benefits of controlling the Lipschitz constant of neural-network models.

Key facts. Cited by 90 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Apr 2018.

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Citing papers per year: 2021: 9; 2022: 11; 2023: 15; 2024: 20; 2025: 15; 2026: 20.

90 papers.

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  1. 2024Beyond A*: Better Planning with Transformers via Search Dynamics Bootstrappingcited by 89
  2. 2022A Survey on Model-based Reinforcement Learningcited by 65
  3. 2025A Comprehensive Survey on World Models for Embodied AIcited by 65
  4. 2021Learning Markov State Abstractions for Deep Reinforcement Learningcited by 42
  5. 2021Mismatched No More: Joint Model-Policy Optimization for Model-Based RLcited by 35
  6. 2023Adaptive Online Replanning with Diffusion Modelscited by 33
  7. 2024LLM-Empowered State Representation for Reinforcement Learningcited by 28
  8. 2023CCIL: Continuity-based Data Augmentation for Corrective Imitation Learningcited by 26
  9. 2024Learning Smooth Humanoid Locomotion through Lipschitz-Constrained Policiescited by 26
  10. 2021NRTSI: Non-Recurrent Time Series Imputationcited by 25
  11. 2021Block Contextual MDPs for Continual Learningcited by 25
  12. 2023Some Fundamental Aspects about Lipschitz Continuity of Neural Networkscited by 25
38 more
  1. 2022Language Control Diffusion: Efficiently Scaling through Space, Time, and Taskscited by 20
  2. 2022Deciding What to Model: Value-Equivalent Sampling for Reinforcement Learningcited by 19
  3. 2023Is Model Ensemble Necessary? Model-based RL via a Single Model with Lipschitz Regularized Value Functioncited by 19
  4. 2023GELU Activation Function in Deep Learning: A Comprehensive Mathematical Analysis and Performancecited by 16
  5. 2022When to Update Your Model: Constrained Model-based Reinforcement Learningcited by 14
  6. 2025Generative Models in Decision Making: A Surveycited by 14
  7. 2021On Effective Scheduling of Model-based Reinforcement Learningcited by 13
  8. 2024Resisting Stochastic Risks in Diffusion Planners with the Trajectory Aggregation Treecited by 13
  9. 2024Learning Variable Compliance Control From a Few Demonstrations for Bimanual Robot with Haptic Feedback Teleoperation Systemcited by 13
  10. 2023Off-Policy RL Algorithms Can be Sample-Efficient for Continuous Control via Sample Multiple Reusecited by 12
  11. 2023Finding Counterfactually Optimal Action Sequences in Continuous State Spacescited by 12
  12. 2025State-Covering Trajectory Stitching for Diffusion Plannerscited by 11
  13. 2023Self-Supervised Reinforcement Learning that Transfers using Random Featurescited by 10
  14. 2025On Rollouts in Model-Based Reinforcement Learningcited by 10
  15. 2023A Bayesian Approach to Robust Inverse Reinforcement Learningcited by 9
  16. 2024Agent-state based policies in POMDPs: Beyond belief-state MDPscited by 9
  17. 2023Planning with Sequence Models through Iterative Energy Minimizationcited by 8
  18. 2024Distributional Successor Features Enable Zero-Shot Policy Optimizationcited by 8
  19. 2024PDE Control Gym: A Benchmark for Data-Driven Boundary Control of Partial Differential Equationscited by 8
  20. 2025Local Manifold Approximation and Projection for Manifold-Aware Diffusion Planningcited by 8
  21. 2021Faster Deep Reinforcement Learning with Slower Online Networkcited by 7
  22. 2023A Survey on Offline Model-Based Reinforcement Learningcited by 7
  23. 2024Model-based Reinforcement Learning for Parameterized Action Spacescited by 7
  24. 2024A Note on Loss Functions and Error Compounding in Model-based Reinforcement Learningcited by 7
  25. 2024An Optimal Tightness Bound for the Simulation Lemmacited by 7
  26. 2022On Rate-Distortion Theory in Capacity-Limited Cognition & Reinforcement Learningcited by 6
  27. 2022Tight Performance Guarantees of Imitator Policies with Continuous Actionscited by 6
  28. 2023Bring Your Own (Non-Robust) Algorithm to Solve Robust MDPs by Estimating The Worst Kernelcited by 6
  29. 2024No-Regret Reinforcement Learning in Smooth MDPscited by 6
  30. 2024Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPscited by 5
  31. 2026The Surprising Difficulty of Search in Model-Based Reinforcement Learningcited by 5
  32. 2021Adversarially Regularized Policy Learning Guided by Trajectory Optimizationcited by 4
  33. 2023Bayesian Reinforcement Learning with Limited Cognitive Loadcited by 4
  34. 2024Long-term Safe Reinforcement Learning with Binary Feedbackcited by 4
  35. 2024Local Linearity: the Key for No-regret Reinforcement Learning in Continuous MDPscited by 4
  36. 2022Truly Deterministic Policy Optimizationcited by 3
  37. 2026WIMLE: Uncertainty-Aware World Models with IMLE for Sample-Efficient Continuous Controlcited by 3
  38. 2026Understanding Rollout Error in Graph World Modelscited by 3

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