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

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6.1 Operators in the parameterised domain \Mop(n,)". There are n operatorsS i for 1 i n : : : : : : : : : : : : : : : : : : : : : : : : : : 816.2 The operators for an example domain. : : : : : : : : : : : : : : : : : 826.3 Operators in the car-starting domain : : : : : : : : : : : : : : : : : : 836.4 Initial tail plan to solve example problem. The directed arcs are causallinks showing that a step establishes a necessary precondition of thestep it points to. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 866.5 A second stage of the planner. There are now two possible currentstates for contexts and . : : : : : : : : : : : : : : : : : : : : : : : 876.6 Atypical plan in the test domain. : : : : : : : : : : : : : : : : : : : : 916.7 Time in seconds to solve planning problem with and without analogyplotted against the number of branches in the conditional plan. Eachpoint isanaverage of ve planning episodes. : : : : : : : : : : : : : : 917.1 Part of the type hierarchy, showing the 52 most important of the 151types in the domain. : : : : : : : : : : : : : : : : : : : : : : : : : : : 957.2 San Francisco Bay area : : : : : : : : : : : : : : : : : : : : : : : : : : 967.3 The exogenous event threatened-shore-changes models the uncertaintyof the oil's path in the water. : : : : : : : : : : : : : : : : : : : 977.4 The exogenous event oil-spills models the uncertain ow of oil fromthe tanker to the sea. : : : : : : : : : : : : : : : : : : : : : : : : : : : 1007.5 The average probability of success for the plans for the randomly generatedproblems, plotted against the number of iterations of improvement.The upper and lower lines show the 90th and 10th percentilesof the probabilities respectively. : : : : : : : : : : : : : : : : : : : : : 1037.6 The number of examples that reach their maximum probability at eachiteration. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1047.7 The graph on the left shows the average improvement gained from eachway to improve a plan across the random set of problems. The graphon the right shows their cumulative contribution to success probability.Although in this domain each conditional branch is generally only 1/4as eective as adding preventing steps, its overall contribution is ahigher proportion because it is used more often. : : : : : : : : : : : : 1047.8 Average probabilities of plans for the same example set, plotted againstthe number of iterations, when Weaver's mechanisms for improvingplan probability are selectively disabled. : : : : : : : : : : : : : : : : 1057.9 Histogram of the percentage of trials whose initial probability of successfell in each of the ten probability ranges 0.1 in width. Roughly halfthe initial cases have probability between 0 and 0.1 : : : : : : : : : : 106xiv
7.10 The lower line shows the mean probability of success plotted against theiteration of Weaver for the cases whose initial probability was between0 and 0.1. The upper line shows these values for the other cases andthe middle line shows the global mean. : : : : : : : : : : : : : : : : : 1067.11 Evolution of probabilities for the initially low probability cases : : : : 1077.12 Evolution of probabilities for the initially high probability cases : : : 1087.13 The event sea-gets-worse. : : : : : : : : : : : : : : : : : : : : : : : 1097.14 The times taken to create the Jensen join tree for the initial plans withsimulated duration less than 12 hours. On the left, explicit event nodeswere used and on the right, Markov chains built using the event graph.Times using the event graph are on average less than one percent oftimes taken with explicit event nodes. : : : : : : : : : : : : : : : : : : 1107.15 The times taken to create the Jensen join tree using Markov chains forall initial plans with simulated duration less than 1,000 hours. : : : : 1117.16 With and without greedy control rules. : : : : : : : : : : : : : : : : : 112xv
Page 1 and 2: Planning under Uncertainty in Dynam
Page 3: AbstractPlanning, the process of nd
Page 6 and 7: 4.3.1 Analysing the belief net and
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Page 12 and 13: 3.12 Reachability graph of literal
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Page 20 and 21: 2 Chapter 1. Introductionif the pri
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Page 24 and 25: 6 Chapter 1. Introductionnet nodes
Page 26 and 27: 8 Chapter 1. Introduction
Page 28 and 29: 10 Chapter 2. Related workIn additi
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46 Chapter 4. The Weaver Algorithmn
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48 Chapter 4. The Weaver AlgorithmB
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50 Chapter 4. The Weaver Algorithm
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70 Chapter 5. Eciency improvements
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118 Chapter 8. Conclusions The appl
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120 Chapter 8. Conclusions
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122 Appendix A. Proofs of theoremso
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124 Appendix A. Proofs of theoremsN
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126 Appendix B. The Oil-spill domai
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158 BIBLIOGRAPHY[Blythe & Veloso 19
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160 BIBLIOGRAPHY[Drummond & Bresina
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162 BIBLIOGRAPHY[Koenig & Simmons 1
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164 BIBLIOGRAPHY[Schoppers 1989b] S
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166 BIBLIOGRAPHY
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