Our work explores the hierarchical structuring of the probabilistic decision models. Potential Hierarchical Decomposition method computes an optimal sequential control strategy for hierarchical search with uncertainty and resource-constraints. We assume that multiple competing hierarchical structures exist in a given domain and a problem space is depicted by an AND/OR graph with the known cost and the distribution of resource consumption for each link. The resource-bounded optimal performance of PHD approach is achieved by controlling the concurrent exploration of these alternative hierarchical structures. The basic algorithm computes an optimal control strategy for conditionally independent (given a state) distributions, has exponential complexity, and is an application of Dynamic Programming. We show that an optimal strategy in the case of uncertain costs depends only on the expected values of costs and not on the whole distributions. The algorithm is extended to handle dependencies and arbitrary interruptability of the actions.there exist an approach that is capable to address simultaneously all these questions?This paper is an attempt to provide such an approach. It describes a Potential Hierarchical Decomposition (PHD) method -a hierarchical planning algorithm for real-time planning with uncertainty. Given an AND/OR graph representation of several alternative problem decompositions, an optimal sequential strategy is computed considering costs of actions and uncertainty in computation times.The resource-bounded optimal performance of PHD approach is achieved by controlling the concurrent exploration of these alternative hierarchical structures. As opposed to classical planners that separate planning and execution phases, a strategy is a conditional plan that includes both planning and execution actions. This conditional plan is computed based on Optimality Principle [Bellman, 19571 using the Stochastic Dynamic Programming [Ross, 19831 approach. The main idea is to base on resource availability the control of concurrent exploration of alternative hierarchical structures. Thus, instead of focusing on the approximate solution of a single exact model, we consider multiple approximations in a modeling phase, and then solve exactly the approximated model. This simple point is worth emphasizing. When coming to approximate solution of a problem, we may choose one of the two obvious alternatives: to approximate the computation, or to replace our problem by another (its approximation) that is easier to solve. In some cases [Dror el al., 881 the approximated model may be drastically simpler to solve, with solution very close to that of the original problems. In this light the various decompositions of the problem are viewed as alternative problem approximations. Simon and Kadane [1975] propose an optimal satisficing search plan. This plan is computed in polynomial time
