On the stability of Lipschitz continuous control problems and its application to reinforcement learning
This work addresses stability issues in reinforcement learning for control problems, offering incremental improvements with theoretical insights and practical algorithm enhancements.
The paper tackles the stability of the Hamilton-Jacobi-Bellman equation in model-free reinforcement learning for Lipschitz continuous control problems, bridging gaps with classical optimal control and proposing a new algorithm that shows improved performance in benchmark tests.
We address the crucial yet underexplored stability properties of the Hamilton--Jacobi--Bellman (HJB) equation in model-free reinforcement learning contexts, specifically for Lipschitz continuous optimal control problems. We bridge the gap between Lipschitz continuous optimal control problems and classical optimal control problems in the viscosity solutions framework, offering new insights into the stability of the value function of Lipschitz continuous optimal control problems. By introducing structural assumptions on the dynamics and reward functions, we further study the rate of convergence of value functions. Moreover, we introduce a generalized framework for Lipschitz continuous control problems that incorporates the original problem and leverage it to propose a new HJB-based reinforcement learning algorithm. The stability properties and performance of the proposed method are tested with well-known benchmark examples in comparison with existing approaches.