Symbolic method for deriving policy in reinforcement learning

This paper addresses the problem of deriving a policy from the value function in the context of reinforcement learning in continuous state and input spaces. We propose a novel method based on genetic programming to construct a symbolic function, which serves as a proxy to the value function and from which a continuous policy is derived. The symbolic proxy function is constructed such that it maximizes the number of correct choices of the control input for a set of selected states. Maximization methods can then be used to derive a control policy that performs better than the policy derived from the original approximate value function. The method was experimentally evaluated on two control problems with continuous spaces, pendulum swing-up and magnetic manipulation, and compared to a standard policy derivation method using the value function approximation. The results show that the proposed method and its variants outperform the standard method.