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

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6 Chapter 1. Introductionnet nodes at one time point were connected to parents at the previous time point,long paths of nodes in the belief net would be created. The time to evaluate thisbelief net would be at least linear in the length of these paths and frequently worse,since belief net evaluation is NP-hard in general [Cooper 1990].One can use the ability to describe exogenous events using Markov chains toescape this diculty. The probability distribution of states in a Markovchain at somefuture time t given the distribution at time 0 can be computed in time logarithmicin t. Methods to dene such Markov chains that guarantee correctness are given inChapter 3. The chains that are computed might have exponential size in the numberof exogenous events in the worst case. The improved time performance in evaluatingthe resulting belief net outweighs the cost of computing the Markov chains when theestablishment intervals vary suciently and the resulting chains are not too large. Ishow in Chapter 7 that there are signicant benets in the oil-spill domain and it islikely that this is the case in a large number of interesting planning domains.Limitations in scopeCreating robust plans under uncertainty is a hard problem that requires a muchbroader set of algorithms and approaches than can be dealt with properly in onethesis. Handling some of the aspects of the problem that have been ignored herewould make avery interesting extension to this work. In particular, the plannerdescribed here does not address plan monitoring or re-planning. After the initial planis created, a complete system would begin to check certain key domain features asthe plan is executed, updating its beliefs that the various alternative courses of actionwill be successful, and revising part or all of the plan if it was deemed necessary. Thepotential need to revise a plan could also aect the initial plan, since an ideal planwould not make early commitments that would reduce later options for revision. Infact the objective measure of a robust plan might include the potential for re-planning.In this thesis the objective measure views the plan as a static, complete object. Whilethe belief net approach lends itself to plan monitoring and belief updates, this aspectis not addressed.Also ignored is the important issue of the source of and condence in the planner'sknowledge about its uncertainty. For example single point probabilities are givenfor each possible action outcome rather than intervals of probability. Again theapproach taken to plan evaluation makes some examination possible of the importanceof the assumptions about uncertainty, via sensitivity analysis, but this has not beenaddressed.1.4 Reader's guide to the thesisThe next chapter surveys some of the related work to this thesis. Chapter 3 describesthe model used to describe planning problems that contain sources of uncertainty.
1.4. Reader's guide to the thesis 7This model is based on the Markov decision process although the planner does notexplicitly build one. Chapter 4 describes the planning algorithm used in Weaver andprovides a simple example. Chapter 5 presents a method to improve the eciency ofevaluating plans, and chapter 6 presents methods to improve the eciency of planningwhen there is uncertainty. Chapter 7 presents an empirical analysis of the planningproblem and the methods to improve eciency in a large planning domain. Finally,chapter 8 summarises the main contributions of the thesis.
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