Decison-Theoretic Refinement Planning using Inheritance Abstraction

Given a probabilistic model of the world and of available actions and a utility function representing the planner’s objectives we wish to find the plan that maximizes expected utility. Finding the optimal plan requires comparing the expected utilities of all possible plans. Doing this explicitly would be computationally prohibitive in all but the smallest of domains. Thus we must find a way to compare partial plans in such a way that we can eliminate some partial plans before fully elaborating them. Such comparisons require a definition of partial plan that allows us to determine that all completions of one plan are less preferred than all completions of another. We achieve such a definition of partial plan by structuring actions into an abstraction hierarchy and by restricting the planner to using only refinement operators. A partial plan is then a plan in which some of the actions are abstract. An abstract plan’s outcomes are sets of outcomes of more concrete plans. Since different probability and utility values may be associated with each specific outcome, in general a probability range and a utility range will be associated with each abstract outcome. Thus the expected utility of an abstract plan is represented by an interval, which includes the expected utilities of all possible instantiations of that abstract plan. Refining the plan, i.e. instantiating on of its actions, tends to narrow the interval. When the expected utility intervals of two plans do not overlap, the one with the lower interval can be eliminated. We present a method for abstracting probabilistic conditionM actions and we show how to compute expected utility bounds for plans containing such abstract actions. We present a planning algorithm that searches through the space of possible plans by building abstract plans, comparing them, and refining only those that might be refinable to the optimal plan. The algorithm is guaranteed to find the optimal plan and with an appropriate abstraction hierarchy has a complexity which is exponentially better than that of exhaustive enumeration. The planning algorithm has been implemented as the DRIPS decision-theoretic refinement planning system. The sys-