Handling Exponential State Space in a POMDP-based Intelligent Tutoring System

An intelligent tutoring system (ITS) is a computer system developed to offer adaptive, one-to-one interactive tutoring. The main modules in an ITS include a student model and a tutoring model. The student model represents and tracks the student´s knowledge and affective states, and the tutoring model decides tutoring actions based on the student´s current states. Partially observable Markov decision process (POMDP) is a useful tool for building It´s. It allows a system to adaptively teach a student even when the student´s states are not completely observable. A core component in a POMDP is a state space that models the student´s states. The space is exponential. When the number of state variables is large, the computational costs become a major barrier to applying POMDP in building It´s. In our research, we develop a new technique for handling the exponential space. In this technique, the pedagogical order of subject concepts is used to partition the space into sub-spaces, and further reduce their sizes. In this paper, we first describe how POMDP can be used for building an ITS and discuss the exponential space problem. We then present our technique in the context of an experimental system. Finally, we present some experimental results.