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The Bellman equation is a core component in the POMDP model, which is an effective tool for handling uncertainty in computer supported teaching. The equation is also a cost bottleneck in implementing a POMDP. The cost to compute it is typically exponential. To build a POMDP-based intelligent tutoring system (ITS) for practical tutoring, we must develop efficient techniques for computing the equation. In this paper, we first analyze the cost in computing the equation, identifying the major factors that contribute to the complexity. We then report our techniques for efficient computing of the Bellman equation. The techniques were developed on the basis of close examination of features of tutoring processes. They are especially suitable for building POMDP-based tutoring systems.

Efficient Computing of the Bellman Equation in a POMDP-based Intelligent Tutoring System