Convergence Properties of a Computational Learning Model for Unknown Markov Chains

Abstract

The increasing complexity of engineering systems has motivated continuing research on computational learning methods toward making autonomous intelligent systems that can learn how to improve their performance over time while interacting with their environment. These systems need not only to sense their environment, but also to integrate information from the environment into all decision-makings. The evolution of such systems is modeled as an unknown controlled Markov chain. In a previous research, the predictive optimal decision-making (POD) model was developed, aiming to learn in real time the unknown transition probabilities and associated costs over a varying finite time horizon. In this paper, the convergence of the POD to the stationary distribution of a Markov chain is proven, thus establishing the POD as a robust model for making autonomous intelligent systems. This paper provides the conditions that the POD can be valid, and be an interpretation of its underlying structure.