Planning under Uncertainty in Dynamic Domains - Carnegie Mellon ...

1.3. Contributions 5A contribution of this thesis is an implemented planner that selectively ignoressome of the sources of uncertainty while choosing actions for the plan, and in aseparate evaluation stage considers the sources that are known to be relevant to thecandidate plan, ignoring others. This process is iterative, with the planner rening itscandidate plan and becoming aware of more sources of uncertainty on each iteration.Using this technique, the planner is the rst to handle uncertain exogenous events.Two further contributions of the thesis are aimed at improving the eciencyof plan creation. First, based on a study of the algorithm a family of domainindependentsearch heuristics is proposed that relax the assumptions of independencetypically made in probabilistic planners, using the observation that the failure of acandidate plan can be used to condition the probability that the modication will besuccessful. Heuristics from this family are demonstrated. Second, a variant ofinternalanalogy is used to reduce the amount of duplicated work in dierent conditionalbranches of the plans produced.Plan evaluationA plan's probability of success is computed by automatically creating a Bayesianbelief net to represent the plan and evaluating it using a standard join tree method[Pearl 1988]. A contribution of this thesis is an algorithm to produce a belief net thatcan be eciently evaluated when there are exogenous events. The algorithm exploitstwo properties that are expected to be common in probabilistic planning domains:a representation for exogenous events that uses stationary probabilities, and a highvariability in the length of establishmentintervals of domain-level properties in plans.The rst property makes it possible to use Markov chains to summarise the actionof exogenous events over time and the second property makes it useful to do so. Ibriey explain this approach below, and describe it in more detail in Chapter 5.In the representation for exogenous events developed in this thesis, events haveprobabilities of occurrence and probability distributions for their possible outcomes.All of these probabilities may depend on the state of the world at the time the eventmay occur, but do not otherwise depend on the time of occurrence. This stationaryproperty of the probabilities makes it possible to dene Markov chains, whose nodesrepresent abstract world states, that can be used to infer the probability of futureabstract world states.The actions that planners consider can often take widely varying amounts of timeto perform. For instance if a planner considers moving a boat or aircraft to a desiredlocation, the action may take from under an hour to several days depending on thecurrent location and state of readiness of the boat or aircraft. Because of thesewide variations, the lengths of time between when the value of a domain variable isestablished in a plan and when it is required can also vary greatly. We call such aninterval of time an establishment interval for the variable. We see that if time weredivided into units of equal length when a belief net is created to evaluate the plan,some establishment intervals would necessarily cross many time units, and if belief