mlsanityData to 14 Oct 2026

Neural Lyapunov Function Approximation with Self-Supervised Reinforcement Learning

arXiv 2503.15629 ↗First posted 19 Mar 2025cs.RO cs.AI cs.CGcited by 1

On the map: Deep reinforcement learning methods → RL theory and sample complexity

Abstract (arXiv)

Control Lyapunov functions are traditionally used to design a controller which ensures convergence to a desired state, yet deriving these functions for nonlinear systems remains a complex challenge. This paper presents a novel, sample-efficient method for neural approximation of nonlinear Lyapunov functions, leveraging self-supervised Reinforcement Learning (RL) to enhance training data generation, particularly for inaccurately represented regions of the state space. The proposed approach employs a data-driven World Model to train Lyapunov functions from off-policy trajectories. The method is validated on both standard and goal-conditioned robotic tasks, demonstrating faster convergence and higher approximation accuracy compared to the state-of-the-art neural Lyapunov approximation baseline. The code is available at: https://github.com/CAV-Research-Lab/SACLA.git

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 24 of its 30 references that are in the map. First posted on arXiv 19 Mar 2025.

Builds on

24 of 30 references.

References · 24

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2018Soft Actor-Critic Algorithms and Applicationscited by 1,240
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12 more
  1. 2022Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environmentscited by 60
  2. 2020Actor-Critic Reinforcement Learning for Control with Stability Guaranteecited by 45
  3. 2022Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guaranteescited by 40
  4. 2020Safe Reinforcement Learning via Projection on a Safe Set: How to Achieve Optimality?cited by 34
  5. 2024Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulationcited by 25
  6. 2023Neural Lyapunov Control for Discrete-Time Systemscited by 23
  7. 2021Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximationcited by 16
  8. 2021Learning Region of Attraction for Nonlinear Systemscited by 16
  9. 2023Data-Driven Control with Inherent Lyapunov Stabilitycited by 6
  10. 2023Learning to Stabilize High-dimensional Unknown Systems Using Lyapunov-guided Explorationcited by 5
  11. 2023Mind the Uncertainty: Risk-Aware and Actively Exploring Model-Based Reinforcement Learningcited by 3
  12. 2022Systematic, Lyapunov-Based, Safe and Stabilizing Controller Synthesis for Constrained Nonlinear Systemscited by 2

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Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025A Review On Safe Reinforcement Learning Using Lyapunov and Barrier Functionscited by 4

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  5. 2024Safe Deep Model-Based Reinforcement Learning with Lyapunov Functions
  6. 2022Generating Stable and Collision-Free Policies through Lyapunov Function Learning
  7. 2026Reinforcement Learning for Control with Probabilistic Stability Guarantee: A Finite-Sample Approach
  8. 2025Robotic World Model: A Neural Network Simulator for Robust Policy Optimization in Robotics