Q-learning based on regularization theory to treat the continuous states and actions

Reinforcement learning is the learning technique to learn how to act optimally in unknown environment through trial and error. Q-learning is one of the famous algorithms for reinforcement learning, but the ordinary Q-learning algorithm using a Q-table has a problem in treating the continuous-valued state and action of the agent. In this paper, a new algorithm that is able to treat the continuous value of the agent´s state and action in Q-learning is presented. This algorithm is based on an approximation method using regularization theory. The Q-function is smoothly approximated by radial basis functions. This algorithm is applied to path planning and control of an inverted pendulum