A probabilistic approach for reducing the search cost in binary decision trees

In many complex problems a particular decision making procedure is often required in order for a final solution to be found. Such a procedure may consist of a large number of intermediate steps where “local” decisions must be taken and can be sometimes represented as a decision tree. When that structure is used the final solutions obtained vary depending on the available information. However, if the same model is applied many times, experimental data can be collected and observations on the acquired knowledge can be made. In this work, we present a probabilistic approach for reducing the number of decisions (tests) that are required in a particular decision making situation. Specifically, we consider that a problem is structured as a complete binary balanced decision tree, the interior nodes of which correspond to decision points; the paths of the tree represent different decision making processes. By assuming that there exists sufficient probabilistic information concerning the decisions-at the interior nodes, we propose techniques in order to minimize the average number of these decisions when we search for a final solution