Solving Hybrid Markov Decision Processes

Abstract

Markov decision processes (MDPs) have developed as a standard for representing uncertainty in decision-theoretic planning. However, MDPs require an explicit representation of the state space and the probabilistic transition model which, in continuous or hybrid continuous-discrete domains, are not always easy to define. Even when this representation is available, the size of the state space and the number of state variables to consider in the transition function may be such that the resulting MDP cannot be solved using traditional techniques. In this paper a reward-based abstraction for solving hybrid MDPs is presented. In the proposed method, we gather information about the rewards and the dynamics of the system by exploring the environment. This information is used to build a decision tree (C4.5) representing a small set of abstract states with equivalent rewards, and then is used to learn a probabilistic transition function using a Bayesian networks learning algorithm (K2). The system output is a problem specification ready for its solution with traditional dynamic programming algorithms. We have tested our abstract MDP model approximation in real-world problem domains. We present the results in terms of the models learned and their solutions for different configurations showing that our approach produces fast solutions with satisfying policies.