Reinforcement learning for robot control using probability density estimations

Abstract

The successful application of Reinforcement Learning (RL) techniques to robot control is limited by the fact that, in most robotic tasks, the state and action spaces are continuous, multidimensional, and in essence, too large for conventional RL algorithms to work. The well known curse of dimensionality makes infeasible using a tabular representation of the value function, which is the classical approach that provides convergence guarantees. When a function approximation technique is used to generalize among similar states, the convergence of the algorithm is compromised, since updates unavoidably affect an extended region of the domain, that is, some situations are modified in a way that has not been really experienced, and the update may degrade the approximation. We propose a RL algorithm that uses a probability density estimation in the joint space of states, actions and Q-values as a means of function approximation. This allows us to devise an updating approach that, taking into account the local sampling density, avoids an excessive modification of the approximation far from the observed sample.