We have studied several possible variations of point-based update. Most of them are based on ideas drawn from the existing literature. None of the variations were able to significantly enhance the effectiveness of the algorithm in accelerating value iteration. Nonetheless a brief discussion of some of them is still worthwhile. The discussion provides further insights about the algorithm and shows how it compares to some of the related work to be discussed in detail in the next section.
The variations can be divide into two categories: those aimed at improving the quality of point-based update and those aimed at reducing complexity. We shall discuss them one by one.