ArticleOpen Access http://dx.doi.org/10.26855/acc.2025.07.009
Stability and Convergence Analysis of Reinforcement Learning Algorithms in Complex Environments
Jifan Zhang
Future Technology School, South China University of Technology, Guangzhou 510000, Guangdong, China.
*Corresponding author: Jifan Zhang
Published: August 21,2025
Abstract
Reinforcement Learning (RL) has demonstrated significant potential in fields such as robotic control, autonomous driving, and financial decision-making. However, in complex environments, RL still faces challenges in stability and convergence. This study addresses this core issue by establishing a theoretical analysis framework that combines stochastic approximation theory and Lyapunov stability theory to rigorously analyze the convergence conditions and stability bounds of various RL algorithms in complex environments. Based on the theoretical analysis, we propose an Adaptive Stable RL (ASRL) algorithm, which employs dynamic regularized policy optimization and robust value function estimation to effectively mitigate policy oscillation and training divergence. Systematic experiments conducted in OpenAI Gym, MuJoCo, and customized non-stationary environments demonstrate that ASRL significantly outperforms baseline algorithms such as PPO and SAC in terms of convergence speed, final performance, and stability. Additionally, in industrial control and robotic navigation case studies, ASRL exhibits excellent adaptability and robustness. This research not only provides theoretical support for RL in complex environments but also offers optimization guidelines for algorithm design in practical applications.
Keywords
Reinforcement learning; Stability analysis; Convergence theory; Non-stationary environments; Adaptive policy optimization; Robust control
References
[1] Zhang Y. Research on mission allocation and trajectory planning algorithms for multi-type UAVs [PhD dissertation]. Harbin: Harbin Institute of Technology; 2023.
[2] Wu Y. Optimization of harbor tugboat scheduling based on a multi-objective hybrid genetic algorithm [Master's thesis]. Xiamen: Xiamen University of Technology; 2023.
[3] Bi M. Research on logarithmic dual-mode blind equalization algorithm for impulsive noise [Master's thesis]. Harbin: Harbin Engineering University; 2024.
[4] Zhang L. Application and optimization of deep reinforcement learning algorithms in autonomous driving systems. J Softw. 2025;46(2):178-80.
[5] Bai Z. Research on reinforcement learning-based path planning algorithms for autonomous mobile robots in complex environments [Master's thesis]. Xi'an: Xi'an University of Technology; 2024.
[6] Song L, Li D, Xu X. Survey on inverse reinforcement learning: algorithms, theory, and applications. Acta Autom Sin. 2024;50(9):1704-23.
[7] Nian C, Jin F, Ma S, et al. Research on heliostat vibration suppression algorithm based on deep reinforcement learning. Noise Vib Control. 2025;45(4):26-31,38.
[8] Zhao K, Li L, Chen Z, et al. Autonomous obstacle avoidance of coal mine underground transportation robot based on intrinsically motivated reinforcement learning algorithm. Ind Mine Autom. 2025;51(6):81-7.
How to cite this paper
Stability and Convergence Analysis of Reinforcement Learning Algorithms in Complex Environments
How to cite this paper: Jifan Zhang. (2025) Stability and Convergence Analysis of Reinforcement Learning Algorithms in Complex Environments. Advances in Computer and Communication, 6(3), 157-161.
DOI: http://dx.doi.org/10.26855/acc.2025.07.009