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64
Planning in Nondeterministic Domains under Partial Observability via Symbolic Model Checking
, 2001
"... Planning under partial observability is one of the most significant and challenging planning problems. It has been ..."
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Cited by 117 (18 self)
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Planning under partial observability is one of the most significant and challenging planning problems. It has been
Planning under continuous time and resource uncertainty: A challenge for AI
 In Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence
, 2002
"... yQSS Group Inc. zQSS Group Inc. xRIACS experiment is assigned a scientific value). Different observations and experiments take differing amounts of time and consume differing amounts of power and data storage.There are, in general, a number of constraints that govern the rovers activities: ffl Ther ..."
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Cited by 102 (16 self)
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yQSS Group Inc. zQSS Group Inc. xRIACS experiment is assigned a scientific value). Different observations and experiments take differing amounts of time and consume differing amounts of power and data storage.There are, in general, a number of constraints that govern the rovers activities: ffl There are time, power, data storage, and positioning constraints for performing different activities. Time constraints often result from illuminationrequirementthat is, experiments may require that a target rock or sample be illuminated with a certain intensity, or from a certain angle.
On the Undecidability of Probabilistic Planning and InfiniteHorizon Partially Observable Markov Decision Problems
, 1999
"... We investigate the computability of problems in probabilistic planning and partially observable infinitehorizon Markov decision processes. The undecidability of the stringexistence problem for probabilistic finite automata is adapted to show that the following problem of plan existence in pr ..."
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Cited by 81 (0 self)
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We investigate the computability of problems in probabilistic planning and partially observable infinitehorizon Markov decision processes. The undecidability of the stringexistence problem for probabilistic finite automata is adapted to show that the following problem of plan existence in probabilistic planning is undecidable: given a probabilistic planning problem, determine whether there exists a plan with success probability exceeding a desirable threshold. Analogous policyexistence problems for partially observable infinitehorizon Markov decision processes under discounted and undiscounted total reward models, averagereward models, and stateavoidance models are all shown to be undecidable. The results apply to corresponding approximation problems as well. 1 Introduction We show that problems in probabilistic planning (Kushmerick, Hanks, & Weld 1995; Boutilier, Dean, & Hanks 1999) and infinitehorizon partially observable Markov decision processes (POMDPs) (L...
On the Undecidability of Probabilistic Planning and Related Stochastic Optimization Problems
 Artificial Intelligence
, 2003
"... Automated planning, the problem of how an agent achieves a goal given a repertoire of actions, is one of the foundational and most widely studied problems in the AI literature. The original formulation of the problem makes strong assumptions regarding the agent's knowledge and control over the world ..."
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Cited by 48 (0 self)
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Automated planning, the problem of how an agent achieves a goal given a repertoire of actions, is one of the foundational and most widely studied problems in the AI literature. The original formulation of the problem makes strong assumptions regarding the agent's knowledge and control over the world, namely that its information is complete and correct, and that the results of its actions are deterministic and known.
Complexity of Planning with Partial Observability
 ICAPS 2004. Proceedings of the Fourteenth International Conference on Automated Planning and Scheduling
, 2004
"... We show that for conditional planning with partial observability the problem of testing existence of plans with success probability 1 is 2EXPcomplete. This result completes the complexity picture for nonprobabilistic propositional planning. We also give new proofs for the EXPhardness of conditio ..."
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Cited by 39 (3 self)
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We show that for conditional planning with partial observability the problem of testing existence of plans with success probability 1 is 2EXPcomplete. This result completes the complexity picture for nonprobabilistic propositional planning. We also give new proofs for the EXPhardness of conditional planning with full observability and the EXPSPACEhardness of conditional planning without observability. The proofs demonstrate how lack of full observability allows the encoding of exponential space Turing machines in the planning problem, and how the necessity to have branching in plans corresponds to the move to a complexity class defined in terms of alternation from the corresponding deterministic complexity class. Lack of full observability necessitates the use of beliefs states, the number of which is exponential in the number of states, and alternation corresponds to the choices a branching plan can make.
Optimal nonmyopic value of information in graphical models  efficient algorithms and theoretical limits
 In Proc. of IJCAI
, 2005
"... Many realworld decision making tasks require us to choose among several expensive observations. In a sensor network, for example, it is important to select the subset of sensors that is expected to provide the strongest reduction in uncertainty. It has been general practice to use heuristicguided ..."
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Cited by 37 (5 self)
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Many realworld decision making tasks require us to choose among several expensive observations. In a sensor network, for example, it is important to select the subset of sensors that is expected to provide the strongest reduction in uncertainty. It has been general practice to use heuristicguided procedures for selecting observations. In this paper, we present the first efficient optimal algorithms for selecting observations for a class of graphical models containing Hidden Markov Models (HMMs). We provide results for both selecting the optimal subset of observations, and for obtaining an optimal conditional observation plan. For both problems, we present algorithms for the filtering case, where only observations made in the past are taken into account, and the smoothing case, where all observations are utilized. Furthermore we prove a surprising result: In most graphical models tasks, if one designs an efficient algorithm for chain graphs, such as HMMs, this procedure can be generalized to polytrees. We prove that the value of information problem is NP PPhard even for discrete polytrees. It also follows from our results that even computing conditional entropies, which are widely used to measure value of information, is a #Pcomplete problem on polytrees. Finally, we demonstrate the effectiveness of our approach on several realworld datasets. 1
MAP Complexity Results and Approximation Methods
 IN PROCEEDINGS OF THE 18TH CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE (UAI
, 2002
"... MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network, given some evidence. MAP appears ..."
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Cited by 35 (2 self)
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MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network, given some evidence. MAP appears
Complexity results and approximation strategies for map explanations
 Journal of Artificial Intelligence Research
, 2004
"... MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation (Pr), or the problem of computing the most probable explanatio ..."
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Cited by 33 (3 self)
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MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation (Pr), or the problem of computing the most probable explanation (MPE). This paper investigates the complexity of MAP in Bayesian networks. Specifically, we show that MAP is complete for NP PP and provide further negative complexity results for algorithms based on variable elimination. We also show that MAP remains hard even when MPE and Pr become easy. For example, we show that MAP is NPcomplete when the networks are restricted to polytrees, and even then can not be effectively approximated. Given the difficulty of computing MAP exactly, and the difficulty of approximating MAP while providing useful guarantees on the resulting approximation, we investigate best effort approximations. We introduce a generic MAP approximation framework. We provide two instantiations of the framework; one for networks which are amenable to exact inference (Pr), and one for networks for which even exact inference is too hard. This allows MAP approximation on networks that are too complex to even exactly solve the easier problems, Pr and MPE. Experimental results indicate that using these approximation algorithms provides much better solutions than standard techniques, and provide accurate MAP estimates in many cases. 1.