mlsanityData to 14 Oct 2026

Reinforcement Learning for Control with Probabilistic Stability Guarantee: A Finite-Sample Approach

arXiv 2603.00043 ↗First posted 9 Feb 2026cs.LG cs.AIcited by 0

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

Abstract (arXiv)

This paper presents a novel approach to reinforcement learning (RL) for control systems that provides probabilistic stability guarantees using finite data. Leveraging Lyapunov's method, we propose a probabilistic stability theorem that ensures mean square stability using only a finite number of sampled trajectories. The probability of stability increases with the number and length of trajectories, converging to certainty as data size grows. Additionally, we derive a policy gradient theorem for stabilizing policy learning and develop an RL algorithm, L-REINFORCE, that extends the classical REINFORCE algorithm to stabilization problems. The effectiveness of L-REINFORCE is demonstrated through simulations on a Cartpole task, where it outperforms the baseline in ensuring stability. This work bridges a critical gap between RL and control theory, enabling stability analysis and controller design in a model-free framework with finite data.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 17 of its 44 references that are in the map. First posted on arXiv 9 Feb 2026.

Builds on

17 of 44 references.

References · 17

  1. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 366
  2. 2018A Lyapunov-based Approach to Safe Reinforcement Learningcited by 297
  3. 2019Lyapunov-based Safe Policy Optimization for Continuous Controlcited by 145
  4. 2020Neural Lyapunov Controlcited by 142
  5. 2021Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functionscited by 94
  6. 2018The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systemscited by 88
  7. 2020Sample Efficient Reinforcement Learning with REINFORCEcited by 86
  8. 2019Finite-Sample Analysis for SARSA with Linear Function Approximationcited by 85
  9. 2019Finite Sample Analysis of Stochastic System Identificationcited by 67
  10. 2019Finite-Sample Analysis of Nonlinear Stochastic Approximation with Applications in Reinforcement Learningcited by 67
  11. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 53
  12. 2020Actor-Critic Reinforcement Learning for Control with Stability Guaranteecited by 45
5 more
  1. 2021Stabilizing Neural Control Using Self-Learned Almost Lyapunov Criticscited by 35
  2. 2021Finite-Sample Analysis of Off-Policy TD-Learning via Generalized Bellman Operatorscited by 17
  3. 2018Stochastic Approximation for Risk-aware Markov Decision Processescited by 10
  4. 2023Learning Stabilization Control from Observations by Learning Lyapunov-like Proxy Modelscited by 10
  5. 2013Global Adaptive Dynamic Programming for Continuous-Time Nonlinear Systemscited by 3

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  1. 2024Stochastic Reinforcement Learning with Stability Guarantees for Control of Unknown Nonlinear Systems
  2. 2024Sampling-based Safe Reinforcement Learning for Nonlinear Dynamical Systems
  3. 2022On Practical Reinforcement Learning: Provable Robustness, Scalability, and Statistical Efficiency
  4. 2024Safe Deep Model-Based Reinforcement Learning with Lyapunov Functions
  5. 2026Sampling-Based Safe Reinforcement Learning
  6. 2025Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functions
  7. 2025Stabilizing Reinforcement Learning with LLMs: Formulation and Practices
  8. 2025R2L: Reliable Reinforcement Learning: Guaranteed Return & Reliable Policies in Reinforcement Learning