Constraint-Based Reasoning
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.
Local entropy as a measure for sampling solutions in Constraint Satisfaction Problems
Baldassi, Carlo, Ingrosso, Alessandro, Lucibello, Carlo, Saglietti, Luca, Zecchina, Riccardo
We introduce a novel Entropy-driven Monte Carlo (EdMC) strategy to efficiently sample solutions of random Constraint Satisfaction Problems (CSPs). First, we extend a recent result that, using a large-deviation analysis, shows that the geometry of the space of solutions of the Binary Perceptron Learning Problem (a prototypical CSP), contains regions of very high-density of solutions. Despite being sub-dominant, these regions can be found by optimizing a local entropy measure. Building on these results, we construct a fast solver that relies exclusively on a local entropy estimate, and can be applied to general CSPs. We describe its performance not only for the Perceptron Learning Problem but also for the random $K$-Satisfiabilty Problem (another prototypical CSP with a radically different structure), and show numerically that a simple zero-temperature Metropolis search in the smooth local entropy landscape can reach sub-dominant clusters of optimal solutions in a small number of steps, while standard Simulated Annealing either requires extremely long cooling procedures or just fails. We also discuss how the EdMC can heuristically be made even more efficient for the cases we studied.
Noisy Tensor Completion via the Sum-of-Squares Hierarchy
In the noisy tensor completion problem we observe $m$ entries (whose location is chosen uniformly at random) from an unknown $n_1 \times n_2 \times n_3$ tensor $T$. We assume that $T$ is entry-wise close to being rank $r$. Our goal is to fill in its missing entries using as few observations as possible. Let $n = \max(n_1, n_2, n_3)$. We show that if $m = n^{3/2} r$ then there is a polynomial time algorithm based on the sixth level of the sum-of-squares hierarchy for completing it. Our estimate agrees with almost all of $T$'s entries almost exactly and works even when our observations are corrupted by noise. This is also the first algorithm for tensor completion that works in the overcomplete case when $r > n$, and in fact it works all the way up to $r = n^{3/2-\epsilon}$. Our proofs are short and simple and are based on establishing a new connection between noisy tensor completion (through the language of Rademacher complexity) and the task of refuting random constant satisfaction problems. This connection seems to have gone unnoticed even in the context of matrix completion. Furthermore, we use this connection to show matching lower bounds. Our main technical result is in characterizing the Rademacher complexity of the sequence of norms that arise in the sum-of-squares relaxations to the tensor nuclear norm. These results point to an interesting new direction: Can we explore computational vs. sample complexity tradeoffs through the sum-of-squares hierarchy?
Automated Regression Testing Using Constraint Programming
Gotlieb, Arnaud (Simula Research Laboratory) | Carlsson, Mats (Swedish Institute in Computer Science) | Liaeen, Marius (CISCO Systems) | Marijan, Dusica (Simula Research Laboratory) | Petillon, Alexandre (Simula Research Laboratory)
In software validation, regression testing aims to check the absence of regression faults in new releases of a software system. Typically, test cases used in regression testing are executed during a limited amount of time and are selected to check a given set of user requirements. When testing large systems, the number of regression tests grows quickly over the years, and yet the available time slot stays limited. In order to overcome this problem, an approach known as test suite reduction (TSR), has been developed in software engineering to select a smallest subset of test cases, so that each requirement remains covered at least once. However solving the TSR problem is difficult as the underlying optimization problem is NP-hard, but it is also crucial for vendors interested in reducing the time to market of new software releases. In this paper, we address regression testing and TSR with Constraint Programming (CP). More specifically, we propose new CP models to solve TSR that exploit global constraints, namely NValue and GCC. We reuse a set of preprocessing rules to reduce a priori each instance, and we introduce a structure-aware search heuristic. We evaluated our CP models and proposed improvements against existing approaches, including a simple greedy approach and MINTS, the state-of-the-art tool of the software engineering community. Our experiments show that CP outperforms both the greedy approach and MINTS when it is interfaced with MiniSAT, in terms of percentage of reduction and execution time. When MINTS is interfaced with CPLEX, we show that our CP model performs better only on percentage of reduction. Finally, by working closely with validation engineers from Cisco Systems, Norway, we integrated our CP model into an industrial regression testing process.