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95
Planning graph heuristics for belief space search
 Journal of Artificial Intelligence Research
, 2006
"... Some recent works in conditional planning have proposed reachability heuristics to improve planner scalability, but many lack a formal description of the properties of their distance estimates. To place previous work in context and extend work on heuristics for conditional planning, we provide a for ..."
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Cited by 84 (13 self)
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Some recent works in conditional planning have proposed reachability heuristics to improve planner scalability, but many lack a formal description of the properties of their distance estimates. To place previous work in context and extend work on heuristics for conditional planning, we provide a formal basis for distance estimates between belief states. We give a definition for the distance between belief states that relies on aggregating underlying state distance measures. We give several techniques to aggregate state distances and their associated properties. Many existing heuristics exhibit a subset of the properties, but in order to provide a standardized comparison we present several generalizations of planning graph heuristics that are used in a single planner. We compliment our belief state distance estimate framework by also investigating efficient planning graph data structures that incorporate BDDs to compute the most effective heuristics. We developed two planners to serve as testbeds for our investigation. The first, CAltAlt, is a conformant regression planner that uses A * search. The second, POND, is a conditional progression planner that uses AO * search. We show the relative effectiveness of our heuristic techniques within these planners. We also compare the performance of these planners with several
Contingent Planning via Heuristic Forward Search with Implicit Belief States
 In ICAPS05
, 2005
"... Contingent planning is the task of generating a conditional plan given uncertainty about the initial state and action effects, but with the ability to observe some aspects of the current world state. Contingent planning can be transformed into an AndOr search problem in belief space, the space wh ..."
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Cited by 73 (4 self)
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Contingent planning is the task of generating a conditional plan given uncertainty about the initial state and action effects, but with the ability to observe some aspects of the current world state. Contingent planning can be transformed into an AndOr search problem in belief space, the space whose elements are sets of possible worlds. In (Brafman & Hoffmann 2004), we introduced a method for implicitly representing a belief state using a propositional formula that describes the sequence of actions leading to that state. This representation trades off space for time and was shown to be quite effective for conformant planning within a heuristic forwardsearch planner based on the FF system. In this paper we apply the same architecture to contingent planning. The changes required to adapt the search space representation are small. More effort is required to adapt the relaxed planning problems whose solution informs the forward search algorithm. We propose the targeted use of an additional relaxation, mapping the relaxed contingent problem into a relaxed conformant problem. Experimental results show that the resulting planning system, ContingentFF, is highly competitive with the stateoftheart contingent planners POND and MBP.
Extending the knowledgebased approach to planning with incomplete information and sensing
 In
, 2004
"... In (Petrick and Bacchus 2002), a “knowledgelevel ” approach to planning under incomplete knowledge and sensing was presented. In comparison with alternate approaches based on representing sets of possible worlds, this higherlevel representation is richer, but the inferences it supports are weaker ..."
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Cited by 55 (7 self)
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In (Petrick and Bacchus 2002), a “knowledgelevel ” approach to planning under incomplete knowledge and sensing was presented. In comparison with alternate approaches based on representing sets of possible worlds, this higherlevel representation is richer, but the inferences it supports are weaker. Nevertheless, because of its richer representation, it is able to solve problems that cannot be solved by alternate approaches. In this paper we examine a collection of new techniques for increasing both the representational and inferential power of the knowledgelevel approach. These techniques have been fully implemented in the PKS (Planning with Knowledge and Sensing) planning system. Taken together they allow us to solve a range of new types of planning problems under incomplete knowledge and sensing.
Compiling Uncertainty Away in Conformant Planning Problems with Bounded Width
"... Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a pathfinding problem in belief space where good belief representations and heuristics are critical for ..."
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Cited by 47 (16 self)
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Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a pathfinding problem in belief space where good belief representations and heuristics are critical for scaling up. In this work, a different formulation is introduced for conformant problems with deterministic actions where they are automatically converted into classical ones and solved by an offtheshelf classical planner. The translation maps literals L and sets of assumptions t about the initial situation, into new literals KL/t that represent that L must be true if t is initially true. We lay out a general translation scheme that is sound and establish the conditions under which the translation is also complete. We show that the complexity of the complete translation is exponential in a parameter of the problem called the conformant width, which for most benchmarks is bounded. The planner based on this translation exhibits good performance in comparison with existing planners, and is the basis for T0, the best performing planner in the Conformant Track of the 2006 International Planning Competition. 1.
From conformant into classical planning: Efficient translations that may be complete too
 ICAPS2007
"... Focusing on the computation of conformant plans whose verification can be done efficiently, we have recently proposed a polynomial scheme for mapping conformant problems P with deterministic actions into classical problems K(P). The scheme is sound as the classical plans are all conformant, but is i ..."
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Cited by 29 (5 self)
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Focusing on the computation of conformant plans whose verification can be done efficiently, we have recently proposed a polynomial scheme for mapping conformant problems P with deterministic actions into classical problems K(P). The scheme is sound as the classical plans are all conformant, but is incomplete as the converse relation does not always hold. In this paper, we extend this work and consider an alternative, more powerful translation based on the introduction of epistemic tagged literals KL/t where L is a literal in P and t is a set of literals in P unknown in the initial situation. The translation ensures that a plan makes KL/t true only when the plan makes L certain in P given the assumption that t is initially true. We show that under general conditions the new translation scheme is complete and that its complexity can be characterized in terms of a parameter of the problem that we call conformant width. We show that the complexity of the translation is exponential in the problem width only, find that the width of almost all benchmarks is 1, and show that a conformant planner based on this translation solves some interesting domains that cannot be solved by other planners. This translation is the basis for T0, the best performing planner
Tractable reasoning with incomplete firstorder knowledge in dynamic systems with contextdependent actions
 In Proc. of IJCAI
, 2005
"... A basic reasoning problem in dynamic systems is the projection problem: determine if a formula holds after a sequence of actions has been performed. In this paper, we propose a tractable1 solution to the projection problem in the presence of incomplete firstorder knowledge and contextdependent a ..."
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Cited by 27 (6 self)
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A basic reasoning problem in dynamic systems is the projection problem: determine if a formula holds after a sequence of actions has been performed. In this paper, we propose a tractable1 solution to the projection problem in the presence of incomplete firstorder knowledge and contextdependent actions. Our solution is based on a type of progression, that is, we progress the initial knowledge base (KB) wrt the action sequence and answer the query against the resulting KB. The form of reasoning we propose is always logically sound and is also logically complete when the query is in a certain normal form and the agent has complete knowledge about the context of any contextdependent actions. 1
Compiling uncertainty away: Solving conformant planning problems using a classical planner (sometimes
 AAAI
, 2006
"... Even under polynomial restrictions on plan length, conformant planning remains a very hard computational problem as plan verification itself can take exponential time. This heavy price cannot be avoided in general although in many cases conformant plans are verifiable efficiently by means of simple ..."
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Cited by 26 (5 self)
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Even under polynomial restrictions on plan length, conformant planning remains a very hard computational problem as plan verification itself can take exponential time. This heavy price cannot be avoided in general although in many cases conformant plans are verifiable efficiently by means of simple forms of disjunctive inference. This raises the question of whether it is possible to identify and use such forms of inference for developing an efficient but incomplete planner capable of solving nontrivial problems quickly. In this work, we show that this is possible by mapping conformant into classical problems that are then solved by an offtheshelf classical planner. The formulation is sound as the classical plans obtained are all conformant, but it is incomplete as the inverse relation does not always hold. The translation accommodates ‘reasoning by cases ’ by means of an ‘splitprotectandmerge’ strategy; namely, atoms L/Xi that represent conditional beliefs ‘if Xi then L ’ are introduced in the classical encoding, that are combined by suitable actions to yield the literal L when the disjunction X1 ∨ · · · ∨ Xn holds and certain invariants in the plan are verified. Empirical results over a wide variety of problems illustrate the power of the approach.
Sequential monte carlo in probabilistic planning reachability heuristics
 Artificial Intelligence
, 2008
"... The current best conformant probabilistic planners encode the problem as a bounded length CSP or SAT problem. While these approaches can find optimal solutions for given plan lengths, they often do not scale for large problems or plan lengths. As has been shown in classical planning, heuristic searc ..."
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Cited by 25 (14 self)
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The current best conformant probabilistic planners encode the problem as a bounded length CSP or SAT problem. While these approaches can find optimal solutions for given plan lengths, they often do not scale for large problems or plan lengths. As has been shown in classical planning, heuristic search outperforms CSP/SAT techniques (especially when a plan length is not given a priori). The problem with applying heuristic search in probabilistic planning is that effective heuristics are as yet lacking. In this work, we apply heuristic search to conformant probabilistic planning by adapting planning graph heuristics developed for nondeterministic planning. We evaluate a straightforward application of these planning graph techniques, which amounts to exactly computing the distribution over reachable relaxed planning graph layers. Computing these distributions is costly, so we apply Sequential Monte Carlo to approximate them. We demonstrate on several domains how our approach enables our planner to far outscale existing (optimal) probabilistic planners and still find reasonable quality solutions.