In this paper, an adaptive reinforcement learning (RL) based controller is developed to solve assistance control problem for Lower Limb Exoskeleton (LLE) to aid hemiplegic individuals in walking. The communication interaction relation between both two lower-limbs and patient's unaffected leg is modelled in the context of leader-follower (LF) framework. The walking assistance control problem of LLE with patients is converted to optimal control problem. To handle the optimal control problem, a discounted cost function is designed in terms of the local tracking error, and then a policy iteration algorithm (PI) is proposed to generate an optimal control policy, followed by the convergence analysis of the presented algorithm. Further, in order to improve the adaption of the controller to different patients, on the basis of the PI algorithm, an actor-critic-based neural network (AC/NN) architecture is introduced to implement the presented control method in an online-learning fashion. Finally, simulation scenarios are established to test the effectiveness of the proposed walking assistance control approaches.