On the stability of Lipschitz continuous control problems and its application to reinforcement learning

arXiv:2404.13316v1 Announce Type: cross
Abstract: 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 …

abstract application arxiv bridge continuous control cs.lg equation free gap hamilton math.ap math.oc reinforcement reinforcement learning stability type