We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. We identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simplify the encoding of a user’s prior knowledge. In particular, a user can express his knowledge—for the most part—as a single prior Bayesian network for the domain. 1

Most databases contain "name constants" like course numbers, personal names, and place names that correspond to entities in the real world. Previous work in integration of heterogeneous databases has assumed that local name constants can be mapped into an appropriate global domain by normalization. However, in many cases, this assumption does not hold; determining if two name constants should be considered identical can require detailed knowledge of the world, the purpose of the user's query, or both. In this paper, we reject the assumption that global domains can be easily constructed, and assume instead that the names are given in natural language text. We then propose a logic called WHIRL which reasons explicitly about the similarity of local names, as measured using the vector-space model commonly adopted in statistical information retrieval. We describe an efficient implementation of WHIRL and evaluate it experimentally on data extracted from the World Wide Web. We show that WHIR...

In the recent AIPS98 Planning Competition, the hsp planner, based on a forward state search and a domain-independent heuristic, showed that heuristic search planners can be competitive with state of the art Graphplan and Satisfiability planners. hsp solved more problems than the other planners but it often took more time or produced longer plans. The main bottleneck in hsp is the computation of the heuristic for every new state. This computation may take up to 85% of the processing time. In this paper, we present a solution to this problem that uses a simple change in the direction of the search. The new planner, that we call hspr, is based on the same ideas and heuristic as hsp, but searches backward from the goal rather than forward from the initial state. This allows hspr to compute the heuristic estimates only once. As a result, hspr can produce better plans, often in less time. For example, hspr solves each of the 30 logistics problems from Kautz and Selman in less than 3 seconds. This is two orders of magnitude faster than blackbox. At the same time

hsp and hspr are two recent planners that search the state-space using an heuristic function extracted from Strips encodings. hsp does a forward search from the initial state recomputing the heuristic in every state, while hspr does a regression search from the goal computing a suitable representation of the heuristic only once. Both planners have shown good performance, often producing solutions that are competitive in time and number of actions with the solutions found by Graphplan and sat planners. hsp and hspr, however, are not optimal planners. This is because the heuristic function is not admissible and the search algorithms are not optimal. In this paper we address this problem. We formulate a new admissible heuristic for planning, use it to guide an ida search, and empirically evaluate the resulting optimal planner over a number of domains. The main contribution is the idea underlying the heuristic that yields not one but a whole family of polynomial and admissible heuristics that trade accuracy for e ciency. The formulation is general and sheds some light on the heuristics used in hsp and Graphplan, and their relation. It exploits the factored (Strips) representation of planning problems, mapping shortest-path problems in state-space into suitably dened shortest-path problems in atom-space. The formulation applies with little variation to sequential and parallel planning, and problems with di erent action costs.

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Many search trees are impractically large to explore exhaustively. Recently, techniques like limited discrepancy search have been proposed for improving the chance of finding a goal in a limited amount of search. Depth-bounded discrepancy search offers such a hope. The motivation behind depth-bounded discrepancy search is that branching heuristics are more likely to be wrong at the top of the tree than at the bottom. We therefore combine one of the best features of limited discrepancy search -- the ability to undo early mistakes -- with the completeness of iterative deepening search. We show theoretically and experimentally that this novel combination outperforms existing techniques. 1 Introduction On backtracking, depth-first search explores decisions made against the branching heuristic (or "discrepancies "), starting with decisions made deep in the search tree. However, branching heuristics are more likely to be wrong at the top of the tree than at the bottom. We would like theref...

Most recent strides in scaling up planning have centered around two competing themes--disjunctive planners, exemplified by Graphplan, and heuristic state search planners, exemplified by UNPOP, HSP and HSP-r. In this paper, we present a novel approach for successfully harnessing the advantages of the two competing paradigms to develop planners that are significantly more powerful than either of the approaches. Specifically, we show that the polynomial-time planning graph structure that the Graphplan builds provides a rich substrate for deriving a family of highly effective heuristics for guiding state space search as well as CSP-style search. The main leverage provided by the planning graph structure is a systematic and graded way to take subgoal interactions into account in designing state space heuristics.

Abstract. The efficiency of A * searching depends on the quality of the lower bound estimates of the solution cost. Pattern databases enumerate all possible subgoals required by any solution, subject to constraints on the subgoal size. Each subgoal in the database provides a tight lower bound on the cost of achieving it. For a given state in the search space, all possible subgoals are looked up, with the maximum cost over all lookups being the lower bound. For sliding tile puzzles, the database enumerates all possible patterns containing N tiles and, for each one, contains a lower bound on the distance to correctly move all N tiles into their correct final location. For the 15-Puzzle, iterative~deepening A * with pattern databases (N=8) reduces the total number of nodes searched on a standard problem set of 100 positions by over 1000-fold. 1

We present an improvement to Harvey and Ginsberg's limited discrepancy search algorithm. Our version eliminates much of the redundancy in the original algorithm, generating each search path from the root to the maximum search depth only once. For a uniform-depth binary tree of depth d, this reduces the asymptotic complexity from O( d+2 2 2 d ) to O(2 d ). The savings is much less in a partial tree search, or in a heavily pruned tree. We also show that the overhead of the improved algorithm on a uniform-depth b-ary tree is only a factor of b=(b\Gamma1) compared to depth-first search. This constant factor is greater on a heavily pruned tree. Finally, we present empirical results showing the utility of limited discrepancy search, as a function of problem difficulty, on the NP-Complete problem of number partitioning. 1 Introduction: Limited Discrepancy Search The best-known tree-search algorithms are breadth-first and depth-first search. Breadth-first search is rarely used in pra...

Planning Cases by Change of Representation Language Ralph Bergmann bergmann@informatik.uni-kl.de Wolfgang Wilke wilke@informatik.uni-kl.de Centre for Learning Systems and Applications (LSA) University of Kaiserslautern, P.O.-Box 3049, D-67653 Kaiserslautern, Germany Abstract Abstraction is one of the most promising approaches to improve the performance of problem solvers. In several domains abstraction by dropping sentences of a domain description -- as used in most hierarchical planners -- has proven useful. In this paper we present examples which illustrate significant drawbacks of abstraction by dropping sentences. To overcome these drawbacks, we propose a more general view of abstraction involving the change of representation language. We have developed a new abstraction methodology and a related sound and complete learning algorithm that allows the complete change of representation language of planning cases from concrete to abstract. However, to achieve a powerful change of th...