Multi-agent planning problems with constraints on global resource consumption occur in several domains. Existing algorithms for solving Multi-agent Markov Decision Processes can compute policies that meet a resource constraint in expectation, but these policies provide no guarantees on the probability that a resource constraint violation will occur. We derive a method to bound constraint violation probabilities using Hoeffding's inequality. This method is applied to two existing approaches for computing policies satisfying constraints: the Constrained MDP framework and a Column Generation approach. We also introduce an algorithm to adaptively relax the bound up to a given maximum violation tolerance. Experiments on a hard toy problem show that the resulting policies outperform static optimal resource allocations to an arbitrary level. By testing the algorithms on more realistic planning domains from the literature, we demonstrate that the adaptive bound is able to efficiently trade off violation probability with expected value, outperforming state-of-the-art planners.

Researchers have used Distributed Constraint Optimization Problems (DCOPs) as a powerful approach to model various multi-agent coordination problems, taking into account their preferences and constraints. A core limitation of this model is the assumption that all agents’ preferences are specified a priori. However, in a number of application domains such knowledge become available only after being elicited from users in these domains. In this abstract, we explore the effects of preference elicitation in our motivating application of scheduling smart appliances with the aim of reducing users’ electricity bill cost as well as increasing their comfort.

We propose to exploit cycles in the constraint network of a Constraint Satisfaction Problem (CSP) to vehicle constraint propagation and improve the effectiveness of local consistency algorithms. We focus our attention on the consistency property Partition-One Arc-Consistency (POAC), which is a stronger variant of Singleton Arc-Consistency (SAC). We modify the algorithm for enforcing POAC to operate on a minimum cycle basis (MCB) of the incidence graph of the CSP. We empirically show that our approach improves the performance of problem solving and constitutes a novel and effective localization of consistency algorithms. Although this paper focuses on POAC, we believe that exploiting cycles, such as MCBs, is applicable to other consistency algorithms and that our study opens a new direction in the design of consistency algorithms. This research is documented in a technical report (Woordward, Choueiry, and Bessiere 2016). http://consystlab.unl.edu/our_work/StudentReports/TR-UNL-CSE-2016-0004.pdf

Potential heuristics for state-space search are defined as weighted sums over simple state features. Atomic features consider the value of a single state variable in a factored state representation, while binary features consider joint assignments to two state variables. Previous work showed that the set of all admissible and consistent potential heuristics using atomic features can be characterized by a compact set of linear constraints. We generalize this result to binary features and prove a hardness result for features of higher dimension. Furthermore, we prove a tractability result based on the treewidth of a new graphical structure we call the context-dependency graph . Finally, we study the relationship of potential heuristics to transition cost partitioning . Experimental results show that binary potential heuristics are significantly more informative than the previously considered atomic ones.

When a small pattern graph does not occur inside a larger target graph, we can ask how to find "as much of the pattern as possible" inside the target graph. In general, this is known as the maximum common subgraph problem, which is much more computationally challenging in practice than subgraph isomorphism. We introduce a restricted alternative, where we ask if all but k vertices from the pattern can be found in the target graph. This allows for the development of slightly weakened forms of certain invariants from subgraph isomorphism which are based upon degree and number of paths.  We show that when k is small, weakening the invariants still retains much of their effectiveness. We are then able to solve this problem on the standard problem instances used to benchmark subgraph isomorphism algorithms, despite these instances being too large for current maximum common subgraph algorithms to handle. Finally, by iteratively increasing k, we obtain an algorithm which is also competitive for the maximum common subgraph

Adding datatypes to ontology-mediated queries (OMQs) often makes query answering hard. As a consequence, the use of datatypes in OWL 2 QL has been severely restricted. In this paper we propose a new, non-uniform, way of analyzing the data-complexity of OMQ answering with datatypes. Instead of restricting the ontology language we aim at a classification of the patterns of datatype atoms in OMQs into those that can occur in non-tractable OMQs and those that only occur in tractable OMQs. To this end we establish a close link between OMQ answering with datatypes and constraint satisfaction problems over the datatypes. In a case study we apply this link to prove a P/coNP-dichotomy for OMQs over DL-Lite extended with the datatype (Q,<=). The proof employs a recent dichotomy result by Bodirsky and Kára for temporal constraint satisfaction problems.

Fine-grained image classification is challenging due to the large intra-class variance and small inter-class variance, aiming at recognizing hundreds of sub-categories belonging to the same basic-level category. Since two different sub-categories is distinguished only by the subtle differences in some specific parts, semantic part localization is crucial for fine-grained image classification. Most previous works improve the accuracy by looking for the semantic parts, but rely heavily upon the use of the object or part annotations of images whose labeling are costly. Recently, some researchers begin to focus on recognizing sub-categories via weakly supervised part detection instead of using the expensive annotations. However, these works ignore the spatial relationship between the object and its parts as well as the interaction of the parts, both of them are helpful to promote part selection. Therefore, this paper proposes a weakly supervised part selection method with spatial constraints for fine-grained image classification, which is free of using any bounding box or part annotations. We first learn a whole-object detector automatically to localize the object through jointly using saliency extraction and co-segmentation. Then two spatial constraints are proposed to select the distinguished parts. The first spatial constraint, called box constraint, defines the relationship between the object and its parts, and aims to ensure that the selected parts are definitely located in the object region, and have the largest overlap with the object region. The second spatial constraint, called parts constraint, defines the relationship of the object's parts, is to reduce the parts' overlap with each other to avoid the information redundancy and ensure the selected parts are the most distinguishing parts from other categories. Combining two spatial constraints promotes parts selection significantly as well as achieves a notable improvement on fine-grained image classification. Experimental results on CUB-200-2011 dataset demonstrate the superiority of our method even compared with those methods using expensive annotations.

Solving constrained combinatorial optimisation problems via MAP inference is often achieved by introducing extra potential functions for each constraint. This can result in very high order potentials, e.g. a 2nd-order objective with pairwise potentials and a quadratic constraint over all N variables would correspond to an unconstrained objective with an order-N potential. This limits the practicality of such an approach, since inference with high order potentials is tractable only for a few special classes of functions. We propose an approach which is able to solve constrained combinatorial problems using belief propagation without increasing the order. For example, in our scheme the 2nd-order problem above remains order 2 instead of order N. Experiments on applications ranging from foreground detection, image reconstruction, quadratic knapsack, and the M-best solutions problem demonstrate the effectiveness and efficiency of our method. Moreover, we show several situations in which our approach outperforms commercial solvers like CPLEX and others designed for specific constrained MAP inference problems.

The 13th International Conference on Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming (CPAIOR 2016), was held in Banff, Canada, May 29 - June 1, 2016. In order to trigger exchanges between the constraint programming and the operations research community, CPAIOR was co-located with CORS 2016, the Canadian Operational Research society's conference.

Logic-based Benders decomposition (LBBD) is a powerful hybrid optimisation technique that can combine the strong dual bounds of mixed integer programming (MIP) with the combinatorial search strengths of constraint programming (CP). A major drawback of LBBD is that it is a far more involved process to implement an LBBD solution to a problem than the "model-and-run" approach provided by both CP and MIP. We propose an automated approach that accepts an arbitrary MiniZinc model and solves it using LBBD with no additional intervention on the part of the modeller. The design of this approach also reveals an interesting duality between LBBD and large neighborhood search (LNS). We compare our implementation of this approach to CP and MIP solvers on 4 different problem classes where LBBD has been applied before.