Stats4Grads: Sequential decision analysis with general choice functions
22 October 2008 14:15 in CM221
Decision trees are useful graphical representations of sequential decision problems. Typically, one of two solution types are used to analyse decision trees: the normal form solution and the extensive form solution. However, common definitions of these solution types are not sufficient to describe all possible approaches to solving decision trees. I shall outline more general definitions for these solution types, which can then describe a much wider variety of solutions, and show that the two forms are fundamentally different.
I shall then consider normal form solutions in more detail. These solutions, in which one initially specifies one's policy for all eventualities, are in theory easy to deal with: one simply needs to compare all available policies and decide which ones are optimal. In practice, there are often too many policies to reasonable compare. This issue can be addressed by extending the usual method of backward induction, which maximizes expected utility, to arbitrary choice functions. We find necessary and sufficient conditions on a choice function under which this method yields the optimal normal form solution.
See the Stats4Grads page for more details about this series.