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Constraint-Based Reasoning


Congratulations to the #IJCAI2020 award winners

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This paper elegantly shows how to automatically construct abstract representations suitable for evaluating plans composed of sequences of high-level actions in a continuous, low-level environment.


On Continuous Local BDD-Based Search for Hybrid SAT Solving

arXiv.org Artificial Intelligence

Constraint-satisfaction problems (CSPs) are fundamental in mathematics, physics, and computer science. The Boolean SATisfiability problem (SAT) is a paradigmatic class of CSPs, where each variable takes value from the binary set {True, False}. Solving SAT efficiently is of utmost significance in computer science, both from a theoretical and a practical perspective. As a special case of SAT, formulas in conjunctive normal form (CNFs) are a conjunction (and-ing) of disjunctions (or-ing) of literals. Despite the NPcompleteness of CNF-SAT, there has been dramatic progress on the engineering side of CNF-SAT solvers [1]. SAT solvers can be classified into complete and incomplete ones: a complete SAT solver will return a solution if there exists one or prove unsatisfiability if no solution exists, while an incomplete algorithm is not guaranteed to find a satisfying assignment nor can it prove unsatisfiability.


Theory-guided hard constraint projection (HCP): a knowledge-based data-driven scientific machine learning method

arXiv.org Artificial Intelligence

Machine learning models have been successfully used in many scientific and engineering fields. However, it remains difficult for a model to simultaneously utilize domain knowledge and experimental observation data. The application of knowledge-based symbolic AI represented by an expert system is limited by the expressive ability of the model, and data-driven connectionism AI represented by neural networks is prone to produce predictions that violate physical mechanisms. In order to fully integrate domain knowledge with observations, and make full use of the prior information and the strong fitting ability of neural networks, this study proposes theory-guided hard constraint projection (HCP). This model converts physical constraints, such as governing equations, into a form that is easy to handle through discretization, and then implements hard constraint optimization through projection. Based on rigorous mathematical proofs, theory-guided HCP can ensure that model predictions strictly conform to physical mechanisms in the constraint patch. The performance of the theory-guided HCP is verified by experiments based on the heterogeneous subsurface flow problem. Due to the application of hard constraints, compared with fully connected neural networks and soft constraint models, such as theory-guided neural networks and physics-informed neural networks, theory-guided HCP requires fewer data, and achieves higher prediction accuracy and stronger robustness to noisy observations.


Computational Complexity of Three Central Problems in Itemset Mining

arXiv.org Artificial Intelligence

Many techniques have been developed for itemset mining problems. Famous examples are mining frequent itemsets (Agrawal et al., 1993; Han et al., 2000), mining association rules (Agrawal et al., 1993; Szathmary et al., 2007), mining closed itemsets(Pasquier et al., 1999), mining high utility itemsets (Chan et al., 2003), etc. Most of these works have focused on improving the practical performance of the mining process, but few have conducted a theoretical analysis of the computational complexity of itemset mining problems. Wijsen and Meersman (1998) have proved that it is NPcomplete to decide whether there exists a valid quantitative rule. Angiulli et al. (2001) have proved that the problem of deciding whether there exists a non-redundant association rule of size at least k that is frequent and the problem of deciding whether there exists a non-redundant association rule of size at least k that is confident are both NPcomplete.


A Knowledge Driven Approach to Adaptive Assistance Using Preference Reasoning and Explanation

arXiv.org Artificial Intelligence

There is a need for socially assistive robots (SARs) to provide transparency in their behavior by explaining their reasoning. Additionally, the reasoning and explanation should represent the user's preferences and goals. To work towards satisfying this need for interpretable reasoning and representations, we propose the robot uses Analogical Theory of Mind to infer what the user is trying to do and uses the Hint Engine to find an appropriate assistance based on what the user is trying to do. If the user is unsure or confused, the robot provides the user with an explanation, generated by the Explanation Synthesizer. The explanation helps the user understand what the robot inferred about the user's preferences and why the robot decided to provide the assistance it gave. A knowledge-driven approach provides transparency to reasoning about preferences, assistance, and explanations, thereby facilitating the incorporation of user feedback and allowing the robot to learn and adapt to the user.


Improving Solution Quality of Bounded Max-Sum Algorithm to Solve DCOPs involving Hard and Soft Constraints

arXiv.org Artificial Intelligence

Bounded Max-Sum (BMS) is a message-passing algorithm that provides approximation solution to a specific form of de-centralized coordination problems, namely Distributed Constrained Optimization Problems (DCOPs). In particular, BMS algorithm is able to solve problems of this type having large search space at the expense of low computational cost. Notably, the traditional DCOP formulation does not consider those constraints that must be satisfied(also known as hard constraints), rather it concentrates only on soft constraints. Hence, although the presence of both types of constraints are observed in a number of real-world applications, the BMS algorithm does not actively capitalize on the hard constraints. To address this issue, we tailor BMS in such a way that can deal with DCOPs having both type constraints. In so doing, our approach improves the solution quality of the algorithm. The empirical results exhibit a marked improvement in the quality of the solutions of large DCOPs.


The Model Counting Competition 2020

arXiv.org Artificial Intelligence

Many computational problems in modern society account to probabilistic reasoning, statistics, and combinatorics. A variety of these real-world questions can be solved by representing the question in (Boolean) formulas and associating the number of models of the formula directly with the answer to the question. Since there has been an increasing interest in practical problem solving for model counting over the last years, the Model Counting (MC) Competition was conceived in fall 2019. The competition aims to foster applications, identify new challenging benchmarks, and to promote new solvers and improve established solvers for the model counting problem and versions thereof. We hope that the results can be a good indicator of the current feasibility of model counting and spark many new applications. In this paper, we report on details of the Model Counting Competition 2020, about carrying out the competition, and the results. The competition encompassed three versions of the model counting problem, which we evaluated in separate tracks. The first track featured the model counting problem (MC), which asks for the number of models of a given Boolean formula. On the second track, we challenged developers to submit programs that solve the weighted model counting problem (WMC). The last track was dedicated to projected model counting (PMC). In total, we received a surprising number of 9 solvers in 34 versions from 8 groups.


Language Generation via Combinatorial Constraint Satisfaction: A Tree Search Enhanced Monte-Carlo Approach

arXiv.org Artificial Intelligence

Generating natural language under complex constraints is a principled formulation towards controllable text generation. We present a framework to allow specification of combinatorial constraints for sentence generation. We propose TSMH, an efficient method to generate high likelihood sentences with respect to a pre-trained language model while satisfying the constraints. Our approach is highly flexible, requires no task-specific training, and leverages efficient constraint satisfaction solving techniques. To better handle the combinatorial constraints, a tree search algorithm is embedded into the proposal process of the Markov chain Monte Carlo (MCMC) to explore candidates that satisfy more constraints. Compared to existing MCMC approaches, our sampling approach has a better mixing performance. Experiments show that TSMH achieves consistent and significant improvement on multiple language generation tasks.


Cable Tree Wiring -- Benchmarking Solvers on a Real-World Scheduling Problem with a Variety of Precedence Constraints

arXiv.org Artificial Intelligence

Cable trees are widely used in industrial products to transmit energy and information between different product parts. For example, cable trees are needed in cars to automate many previously mechanical functions such as moving seats or opening windows and to add new functions such as a voice-controlled navigation or an onboard entertainment system. It is thus not surprising that for example a car like the VW Golf 7 contains 14 cable trees with a total of 1633 cables. The manufacturing of cable trees usually relies on cheap manual labour performed in low-cost countries where humans plug cables into harnesses following a wiring plan. Only few automated manufacturing solutions exist, which rely on complex robotic machines. These machines execute a sequence of wiring operations that highly qualified technicians develop by analyzing the wiring plan. With the continuing tendency towards customer-specific and resource-efficient justin-time manufacturing, smaller batch sizes of cable trees need to be manufactured requiring a frequent change of wiring plans, for which wiring sequences should be derived instantly. Scaling up human expertise to such frequent changes is simply impossible, which explains a growing interest in the intelligent automated manufacturing of cable trees. This interest is also nourished by a further miniaturization of cable harnesses, which will make their manual manufacturing impossible.


Online Learning Based Risk-Averse Stochastic MPC of Constrained Linear Uncertain Systems

arXiv.org Machine Learning

This paper investigates the problem of designing data-driven stochastic Model Predictive Control (MPC) for linear time-invariant systems under additive stochastic disturbance, whose probability distribution is unknown but can be partially inferred from data. We propose a novel online learning based risk-averse stochastic MPC framework in which Conditional Value-at-Risk (CVaR) constraints on system states are required to hold for a family of distributions called an ambiguity set. The ambiguity set is constructed from disturbance data by leveraging a Dirichlet process mixture model that is self-adaptive to the underlying data structure and complexity. Specifically, the structural property of multimodality is exploit-ed, so that the first- and second-order moment information of each mixture component is incorporated into the ambiguity set. A novel constraint tightening strategy is then developed based on an equivalent reformulation of distributionally ro-bust CVaR constraints over the proposed ambiguity set. As more data are gathered during the runtime of the controller, the ambiguity set is updated online using real-time disturbance data, which enables the risk-averse stochastic MPC to cope with time-varying disturbance distributions. The online variational inference algorithm employed does not require all collected data be learned from scratch, and therefore the proposed MPC is endowed with the guaranteed computational complexity of online learning. The guarantees on recursive feasibility and closed-loop stability of the proposed MPC are established via a safe update scheme. Numerical examples are used to illustrate the effectiveness and advantages of the proposed MPC.