Constraint-Based Reasoning
Parallel Model-Based Diagnosis on Multi-Core Computers
Jannach, Dietmar, Schmitz, Thomas, Shchekotykhin, Kostyantyn
Model-Based Diagnosis (MBD) is a principled and domain-independent way of analyzing why a system under examination is not behaving as expected. Given an abstract description (model) of the system's components and their behavior when functioning normally, MBD techniques rely on observations about the actual system behavior to reason about possible causes when there are discrepancies between the expected and observed behavior. Due to its generality, MBD has been successfully applied in a variety of application domains over the last decades. In many application domains of MBD, testing different hypotheses about the reasons for a failure can be computationally costly, e.g., because complex simulations of the system behavior have to be performed. In this work, we therefore propose different schemes of parallelizing the diagnostic reasoning process in order to better exploit the capabilities of modern multi-core computers. We propose and systematically evaluate parallelization schemes for Reiter's hitting set algorithm for finding all or a few leading minimal diagnoses using two different conflict detection techniques. Furthermore, we perform initial experiments for a basic depth-first search strategy to assess the potential of parallelization when searching for one single diagnosis. Finally, we test the effects of parallelizing "direct encodings" of the diagnosis problem in a constraint solver.
Learning Constraints and Optimization Criteria
While there exist several approaches in the constraint programming community to learn a constraint theory, few of them have considered the learning of constraint optimization problems.To alleviate this situation, we introduce an initial approach to learning first-order weighted MAX-SAT theories. It employs inductive logic programming techniques to learn a set of first-order clauses and then uses preference learning techniques to learn the weights of the clauses.In order to learn these weighted clauses, the clausal optimization system uses examples of possible worlds and a set of preferences that state which examples are preferred over other ones.The technique is also empirically evaluated on a number of examples.These experiments show that the system is capable of learning clauses and weights that accurately capture underlying models.
Constrained Sampling and Counting: Universal Hashing Meets SAT Solving
Meel, Kuldeep S. (Rice University) | Vardi, Moshe Y. (Rice University) | Chakraborty, Supratik (Indian Institute of Technology, Bombay) | Fremont, Daniel J. (University of California, Berkeley) | Seshia, Sanjit A. (University of California, Berkeley) | Fried, Dror (Rice University) | Ivrii, Alexander (IBM Research, Haifa) | Malik, Sharad (Princeton University)
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these problems was thoroughly investigated in the 1980s, prior work either did not scale to industrial size instances or gave up correctness guarantees to achieve scalability. Recently, we proposed a novel approach that combines universal hashing and SAT solving and scales to formulas with hundreds of thousands of variables without giving up correctness guarantees. This paper provides an overview of the key ingredients of the approach and discusses challenges that need to be overcome to handle larger real-world instances.
Proactive Dynamic DCOPs
Hoang, Khoi (New Mexico State University) | Fioretto, Ferdinando ( New Mexico State University ) | Hou, Ping ( New Mexico State University ) | Yokoo, Makoto ( Kyushu University ) | Yeoh, William ( New Mexico State University ) | Zivan, Roie ( Ben-Gurion University )
The current approaches to model dynamism in DCOPs solve a sequence of static problems, reacting to the changes in the environment as the agents observe them. Such approaches, thus, ignore possible predictions on the environment evolution. To overcome such limitations, we introduce the Proactive Dynamic DCOP (PD-DCOP) model, a novel formalism to model dynamic DCOPs in the presence of exogenous uncertainty. In contrast to reactive approaches, PD-DCOPs are able to explicitly model the possible changes to the problem, and take such information into account proactively, when solving the dynamically changing problem.
Bayesian Markov Games with Explicit Finite-Level Types
Chandrasekaran, Muthukumaran (University of Georgia) | Chen, Yingke (University of Georgia) | Doshi, Prashant (University of Georgia)
We present a new game-theoretic framework where Bayesian players engage in a Markov game and each has private but imperfect information regarding other players' types. Instead of utilizing Harsanyi's abstract types and a common prior distribution, we construct player types whose structure is explicit and induces a finite level belief hierarchy. We characterize equilibria in this game and formalize the computation of finding such equilibria as a constraint satisfaction problem. The effectiveness of the new framework is demonstrated on two ad hoc team work domains.
Constructive Geometric Constraint Solving as a General Framework for KR-Based Declarative Spatial Reasoning
Schultz, Carl (University of Muenster) | Bhatt, Mehul (University of Bremen)
We present a robust and scalable KR-centered foundation for modularly supporting general declarative spatial representation and reasoning within diverse declarative programming AI frameworks. Based on Constructive Geometric Constraint Solving, our approach provides the foundations for mixed qualitative-quantitative reasoning about space - mereotopology, relative orientation, size, proximity - encompassing key application-driven capabilities such as qualification, spatial consistency solving, quantification, and dynamic geometry. The paper also demonstrates: (a) the framework with benchmark problems (e.g., contact and orientation problems) and applications in spatial Q/A; (b) integration with constraint logic programming, and (c) empirical results illustrating how the proposed encodings outperform existing methods by orders of magnitude on the selected problems.
On Declarative Modeling of Structured Pattern Mining
Guns, Tias (KU Leuven) | Paramonov, Sergey (KU Leuven) | Negrevergne, Benjamin (Inria Rennes)
Since the seminal work on frequent itemset mining, there has been considerable effort on mining more structured patterns such as sequences or graphs. Additionally, the field of constraint programming has been linked to the field of pattern mining resulting in a more general and declarative constraint-based itemset mining framework. As a result, a number of recent papers have proposed to extend the declarative approach to structured pattern mining problems. Because the formalism and the solving mechanisms can be vastly different in specialised algorithm and declarative approaches, assessing the benefits and the drawbacks of each approach can be difficult. In this paper, we introduce a framework that formally defines the core components of itemset, sequence and graph mining tasks, and we use it to compare existing specialised algorithms to their declarative counterpart. This analysis allows us to draw clear connections between the two approaches and provide insights on how to overcome current limitations in declarative structured mining.
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ASlib: A Benchmark Library for Algorithm Selection
Bischl, Bernd, Kerschke, Pascal, Kotthoff, Lars, Lindauer, Marius, Malitsky, Yuri, Frechette, Alexandre, Hoos, Holger, Hutter, Frank, Leyton-Brown, Kevin, Tierney, Kevin, Vanschoren, Joaquin
The task of algorithm selection involves choosing an algorithm from a set of algorithms on a per-instance basis in order to exploit the varying performance of algorithms over a set of instances. The algorithm selection problem is attracting increasing attention from researchers and practitioners in AI. Years of fruitful applications in a number of domains have resulted in a large amount of data, but the community lacks a standard format or repository for this data. This situation makes it difficult to share and compare different approaches effectively, as is done in other, more established fields. It also unnecessarily hinders new researchers who want to work in this area. To address this problem, we introduce a standardized format for representing algorithm selection scenarios and a repository that contains a growing number of data sets from the literature. Our format has been designed to be able to express a wide variety of different scenarios. Demonstrating the breadth and power of our platform, we describe a set of example experiments that build and evaluate algorithm selection models through a common interface. The results display the potential of algorithm selection to achieve significant performance improvements across a broad range of problems and algorithms.
An Exact Algorithm Based on MaxSAT Reasoning for the Maximum Weight Clique Problem
Fang, Zhiwen, Li, Chu-Min, Xu, Ke
Recently, MaxSAT reasoning is shown very effective in computing a tight upper bound for a Maximum Clique (MC) of a (unweighted) graph. In this paper, we apply MaxSAT reasoning to compute a tight upper bound for a Maximum Weight Clique (MWC) of a wighted graph. We first study three usual encodings of MWC into weighted partial MaxSAT dealing with hard clauses, which must be satisfied in all solutions, and soft clauses, which are weighted and can be falsified. The drawbacks of these encodings motivate us to propose an encoding of MWC into a special weighted partial MaxSAT formalism, called LW (Literal-Weighted) encoding and dedicated for upper bounding an MWC, in which both soft clauses and literals in soft clauses are weighted. An optimal solution of the LW MaxSAT instance gives an upper bound for an MWC, instead of an optimal solution for MWC. We then introduce two notions called the Top-k literal failed clause and the Top-k empty clause to extend classical MaxSAT reasoning techniques, as well as two sound transformation rules to transform an LW MaxSAT instance. Successive transformations of an LW MaxSAT instance driven by MaxSAT reasoning give a tight upper bound for the encoded MWC. The approach is implemented in a branch-and-bound algorithm called MWCLQ. Experimental evaluations on the broadly used DIMACS benchmark, BHOSLIB benchmark, random graphs and the benchmark from the winner determination problem show that our approach allows MWCLQ to reduce the search space significantly and to solve MWC instances effectively. Consequently, MWCLQ outperforms state-of-the-art exact algorithms on the vast majority of instances. Moreover, it is surprisingly effective in solving hard and dense instances.