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298
AND/OR branchandbound search for combinatorial optimization in graphical models
, 2008
"... We introduce a new generation of depthfirst BranchandBound algorithms that explore the AND/OR search tree using static and dynamic variable orderings for solving general constraint optimization problems. The virtue of the AND/OR representation of the search space is that its size may be far small ..."
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Cited by 39 (19 self)
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We introduce a new generation of depthfirst BranchandBound algorithms that explore the AND/OR search tree using static and dynamic variable orderings for solving general constraint optimization problems. The virtue of the AND/OR representation of the search space is that its size may be far smaller than that of a traditional OR representation, which can translate into significant time savings for search algorithms. The focus of this paper is on linear space search which explores the AND/OR search tree rather than the search graph and therefore make no attempt to cache information. We investigate the power of the minibucket heuristics within the AND/OR search space, in both static and dynamic setups. We focus on two most common optimization problems in graphical models: finding the Most Probable Explanation (MPE) in Bayesian networks and solving Weighted CSPs (WCSP). In extensive empirical evaluations we demonstrate that the new AND/OR BranchandBound approach improves considerably over the traditional OR search strategy and show how various variable ordering schemes impact the performance of the AND/OR search scheme.
Open constraint programming
 ARTIFICIAL INTELLIGENCE 161 (2005) 181–208
, 2005
"... Traditionally, constraint satisfaction problems (CSP) have assumed closedworld scenarios where all domains and constraints are fixed from the beginning. With the Internet, many of the traditional CSP applications in resource allocation, scheduling and planning pose themselves in openworld settings ..."
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Cited by 38 (5 self)
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Traditionally, constraint satisfaction problems (CSP) have assumed closedworld scenarios where all domains and constraints are fixed from the beginning. With the Internet, many of the traditional CSP applications in resource allocation, scheduling and planning pose themselves in openworld settings, where domains and constraints must be discovered from different sources in a network. To model this scenario, we define open constraint satisfaction problems (OCSP) as CSP where domains and constraints are incrementally discovered through a network. We then extend the concept to open constraint optimization (OCOP). OCSP can be solved without complete knowledge of the variable domains, and we give sound and complete algorithms. We show that OCOP require the additional assumption that variable domains and relations are revealed in nondecreasing order of preference. We present a variety of algorithms for solving OCOP in the possibilistic and weighted model. We compare the algorithms through experiments on randomly generated problems. We show that in certain cases, open constraint programming can require significantly less information than traditional methods where gathering information and solving the CSP are separated. This leads to a reduction in network traffic and server load, and improves privacy in distributed problem solving.
Approximate linear programming for firstorder MDPs
 In Proc. UAI05, 509– 517
, 2005
"... We introduce a new approximate solution technique for firstorder Markov decision processes (FOMDPs). Representing the value function linearly w.r.t. a set of firstorder basis functions, we compute suitable weights by casting the corresponding optimization as a firstorder linear program and show h ..."
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Cited by 37 (9 self)
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We introduce a new approximate solution technique for firstorder Markov decision processes (FOMDPs). Representing the value function linearly w.r.t. a set of firstorder basis functions, we compute suitable weights by casting the corresponding optimization as a firstorder linear program and show how offtheshelf theorem prover and LP software can be effectively used. This technique allows one to solve FOMDPs independent of a specific domain instantiation; furthermore, it allows one to determine bounds on approximation error that apply equally to all domain instantiations. We apply this solution technique to the task of elevator scheduling with a rich feature space and multicriteria additive reward, and demonstrate that it outperforms a number of intuitive, heuristicallyguided policies. 1
SampleSearch: Importance Sampling in Presence of Determinism
, 2009
"... The paper focuses on developing effective importance sampling algorithms for mixed probabilistic and deterministic graphical models. The use of importance sampling in such graphical models is problematic because it generates many useless zero weight samples which are rejected yielding an inefficient ..."
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Cited by 36 (4 self)
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The paper focuses on developing effective importance sampling algorithms for mixed probabilistic and deterministic graphical models. The use of importance sampling in such graphical models is problematic because it generates many useless zero weight samples which are rejected yielding an inefficient sampling process. To address this rejection problem, we propose the SampleSearch scheme that augments sampling with systematic constraintbased backtracking search. We characterize the bias introduced by the combination of search with sampling, and derive a weighting scheme which yields an unbiased estimate of the desired statistics (e.g. probability of evidence). When computing the weights exactly is too complex, we propose an approximation which has a weaker guarantee of asymptotic unbiasedness. We present results of an extensive empirical evaluation demonstrating that SampleSearch outperforms other schemes in presence of significant amount of determinism.
Probabilistic argumentation systems: a new perspective on DempsterShafer theory
 International Journal of Intelligent Systems, Special Issue on the DempsterShafer Theory of Evidence
, 2003
"... The goal of this paper is to study the connection between DempsterShafer theory and probabilistic argumentation systems. By introducing a general method to translate probabilistic argumentation systems into corresponding DempsterShafer belief potentials, its contribution is twofold. On the one han ..."
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Cited by 35 (13 self)
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The goal of this paper is to study the connection between DempsterShafer theory and probabilistic argumentation systems. By introducing a general method to translate probabilistic argumentation systems into corresponding DempsterShafer belief potentials, its contribution is twofold. On the one hand, the paper proposes probabilistic argumentation systems as a convenient and powerful modeling language to be put on top of DempsterShafer theory. On the other hand, it shows how to use DempsterShafer theory as an efficient computational tool for numerical computations in probabilistic argumentation systems. 1
A General Scheme for Automatic Generation of Search Heuristics from Specification Dependencies
 Artificial Intelligence
, 2001
"... The paper presents and evaluates the power of a new scheme that generates search heuristics mechanically for problems expressed using a set of functions or relations over a finite set of variables. The heuristics are extracted from a parameterized approximation scheme called MiniBucket eliminati ..."
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Cited by 34 (17 self)
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The paper presents and evaluates the power of a new scheme that generates search heuristics mechanically for problems expressed using a set of functions or relations over a finite set of variables. The heuristics are extracted from a parameterized approximation scheme called MiniBucket elimination that allows controlled tradeoff between computation and accuracy. The heuristics are used to guide BranchandBound and BestFirst search. Their performance is compared on two optimization tasks: the MaxCSP task defined on deterministic databases and the Most Probable Explanation task defined on probabilistic databases. Benchmarks were random data sets as well as applications to coding and medical diagnosis problems. Our results demonstrate that the heuristics generated are effective for both search schemes, permitting controlled tradeoff between preprocessing (for heuristic generation) and search.
Concurrent hierarchical reinforcement learning
, 2005
"... We describe a language for partially specifying policies in domains consisting of multiple subagents working together to maximize a common reward function. The language extends ALisp with constructs for concurrency and dynamic assignment of subagents to tasks. During learning, the subagents learn a ..."
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Cited by 34 (0 self)
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We describe a language for partially specifying policies in domains consisting of multiple subagents working together to maximize a common reward function. The language extends ALisp with constructs for concurrency and dynamic assignment of subagents to tasks. During learning, the subagents learn a distributed representation of the Qfunction for this partial policy. They then coordinate at runtime to find the best joint action at each step. We give examples showing that programs in this language are natural and concise. We also describe online and batch learning algorithms for learning a linear approximation to the Qfunction, which make use of the coordination structure of the problem.
Simulating quantum computation by contracting tensor networks
 SIAM Journal on Computing
, 2005
"... The treewidth of a graph is a useful combinatorial measure of how close the graph is to a tree. We prove that a quantum circuit with T gates whose underlying graph has treewidth d can be simulated deterministically in T O(1) exp[O(d)] time, which, in particular, is polynomial in T if d = O(logT). Am ..."
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Cited by 32 (1 self)
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The treewidth of a graph is a useful combinatorial measure of how close the graph is to a tree. We prove that a quantum circuit with T gates whose underlying graph has treewidth d can be simulated deterministically in T O(1) exp[O(d)] time, which, in particular, is polynomial in T if d = O(logT). Among many implications, we show efficient simulations for quantum formulas, defined and studied by Yao (Proceedings of the 34th Annual Symposium on Foundations of Computer Science, 352–361, 1993), and for logdepth circuits whose gates apply to nearby qubits only, a natural constraint satisfied by most physical implementations. We also show that oneway quantum computation of Raussendorf and Briegel (Physical Review Letters, 86:5188– 5191, 2001), a universal quantum computation scheme with promising physical implementations, can be efficiently simulated by a randomized algorithm if its quantum resource is derived from a smalltreewidth graph.
Solving Factored POMDPs with Linear Value Functions
 In IJCAI01 workshop on Planning under Uncertainty and Incomplete Information
, 2001
"... Partially Observable Markov Decision Processes (POMDPs) provide a coherent mathematical framework for planning under uncertainty when the state of the system cannot be fully observed. However, the problem of finding an exact POMDP solution is intractable. ..."
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Cited by 32 (2 self)
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Partially Observable Markov Decision Processes (POMDPs) provide a coherent mathematical framework for planning under uncertainty when the state of the system cannot be fully observed. However, the problem of finding an exact POMDP solution is intractable.
Bayesian Inference in the Presence of Determinism
 In AISTATS2003
, 2003
"... In this paper, we consider the problem of performing inference on Bayesian networks which exhibit a substantial degree of determinism. ..."
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Cited by 30 (10 self)
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In this paper, we consider the problem of performing inference on Bayesian networks which exhibit a substantial degree of determinism.