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Learning Variable Ordering Heuristics for Solving Constraint Satisfaction Problems

arXiv.org Artificial Intelligence

Abstract--Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are handcrafted based on expert knowledge. In this paper, we propose a deep reinforcement learning based approach to automatically discover new variable ordering heuristics that are better adapted for a given class of CSP instances. We show that directly optimizing the search cost is hard for bootstrapping, and propose to optimize the expected cost of reaching a leaf node in the search tree. T o capture the complex relations among the variables and constraints, we design a representation scheme based on Graph Neural Network that can process CSP instances with different sizes and constraint arities. Experimental results on random CSP instances show that the learned policies outperform classical handcrafted heuristics in terms of minimizing the search tree size, and can effectively generalize to instances that are larger than those used in training. Constraint Satisfaction Problem (CSP) is one of the most widely studied problems in computer science and artificial intelligence. It provides a common framework for modeling and solving combinatorial problems in many application domains, such as planning and scheduling [1], [2], vehicle routing [3], [4], graph problems [5], [6], and computational biology [7], [8]. A CSP instance involves a set of variables and constraints. T o solve it, one needs to find a value assignment for all variables such that all constraints are satisfied, or prove such assignment does not exist. Despite its ubiquitous applications, unfortunately, CSP is well known to be NPcomplete in general [9]. T o solve CSP efficiently, backtracking search algorithms are often employed, which are exact algorithms with the guarantee that a solution will be found if one exists.


The Ambiguous World of Emotion Representation

arXiv.org Artificial Intelligence

Artificial intelligence and machine learning systems have demonstrated huge improvements and human-level parity in a range of activities, including speech recognition, face recognition and speaker verification. However, these diverse tasks share a key commonality that is not true in affective computing: the ground truth information that is inferred can be unambiguously represented. This observation provides some hints as to why affective computing, despite having attracted the attention of researchers for years, may not still be considered a mature field of research. A key reason for this is the lack of a common mathematical framework to describe all the relevant elements of emotion representations. This paper proposes the AMBiguous Emotion Representation (AMBER) framework to address this deficiency. AMBER is a unified framework that explicitly describes categorical, numerical and ordinal representations of emotions, including time varying representations. In addition to explaining the core elements of AMBER, the paper also discusses how some of the commonly employed emotion representation schemes can be viewed through the AMBER framework, and concludes with a discussion of how the proposed framework can be used to reason about current and future affective computing systems.


Multi-modal space structure: a new kind of latent correlation for multi-modal entity resolution

arXiv.org Artificial Intelligence

Multi-modal data is becoming more common than before because of big data issues. Finding the semantically equal or similar objects from different data sources(called entity resolution) is one of the heart problem of multi-modal task. Current models for solving this problem usually needs much paired data to find the latent correlation between multi-modal data, which is of high cost. A new kind latent correlation is proposed in this article. With the correlation, multi-modal objects can be uniformly represented in a commonly shard space. A classifying based model is designed for multi-modal entity resolution task. With the proposed method, the demand of training data can be decreased much.


Moral Decision Making Frameworks for Artificial Intelligence

AAAI Conferences

The generality of decision and game theory has enabled domain-independent progress in AI research. For example, a better algorithm for finding good policies in (PO)MDPs can be instantly used in a variety of applications. But such a general theory is lacking when it comes to moral decision making. For AI applications with a moral component, are we then forced to build systems based on many ad-hoc rules? In this paper we discuss possible ways to avoid this conclusion.


Learning Concept Graphs from Online Educational Data

Journal of Artificial Intelligence Research

This paper addresses an open challenge in educational data mining, i.e., the problem of automatically mapping online courses from different providers (universities, MOOCs, etc.) onto a universal space of concepts, and predicting latent prerequisite dependencies (directed links) among both concepts and courses. We propose a novel approach for inference within and across course-level and concept-level directed graphs. In the training phase, our system projects partially observed course-level prerequisite links onto directed concept-level links; in the testing phase, the induced concept-level links are used to infer the unknown course-level prerequisite links. Whereas courses may be specific to one institution, concepts are shared across different providers. The bi-directional mappings enable our system to perform interlingua-style transfer learning, e.g. treating the concept graph as the interlingua and transferring the prerequisite relations across universities via the interlingua. Experiments on our newly collected datasets of courses from MIT, Caltech, Princeton and CMU show promising results.


Coupled Interdependent Attribute Analysis on Mixed Data

AAAI Conferences

In the real-world applications, heterogeneous interdependent attributes that consist of both discrete and numerical variables can be observed ubiquitously. The usual representation of these data sets is an information table, assuming the independence of attributes. However, very often, they are actually interdependent on one another, either explicitly or implicitly. Limited research has been conducted in analyzing such attribute interactions, which causes the analysis results to be more local than global. This paper proposes the coupled heterogeneous attribute analysis to capture the interdependence among mixed data by addressing coupling context and coupling weights in unsupervised learning. Such global couplings integrate the interactions within discrete attributes, within numerical attributes and across them to form the coupled representation for mixed type objects based on dimension conversion and feature selection. This work makes one step forward towards explicitly modeling the interdependence of heterogeneous attributes among mixed data, verified by the applications in data structure analysis, data clustering evaluation, and density comparison. Substantial experiments on 12 UCI data sets show that our approach can effectively capture the global couplings of heterogeneous attributes and outperforms the state-of-the-art methods, supported by statistical analysis.


Discrete Dynamical Genetic Programming in XCS

arXiv.org Artificial Intelligence

A number of representation schemes have been presented for use within Learning Classifier Systems, ranging from binary encodings to neural networks. This paper presents results from an investigation into using a discrete dynamical system representation within the XCS Learning Classifier System. In particular, asynchronous random Boolean networks are used to represent the traditional condition-action production system rules. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such discrete dynamical systems within XCS to solve a number of well-known test problems.


Fuzzy Dynamical Genetic Programming in XCSF

arXiv.org Artificial Intelligence

A number of representation schemes have been presented for use within Learning Classifier Systems, ranging from binary encodings to Neural Networks, and more recently Dynamical Genetic Programming (DGP). This paper presents results from an investigation into using a fuzzy DGP representation within the XCSF Learning Classifier System. In particular, asynchronous Fuzzy Logic Networks are used to represent the traditional condition-action production system rules. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such fuzzy dynamical systems within XCSF to solve several well-known continuous-valued test problems.



Practical Issues in Temporal Difference Learning

Neural Information Processing Systems

This paper examines whether temporal difference methods for training connectionist networks, such as Suttons's TO('\) algorithm, can be successfully appliedto complex real-world problems. A number of important practical issues are identified and discussed from a general theoretical perspective. Thesepractical issues are then examined in the context of a case study in which TO('\) is applied to learning the game of backgammon from the outcome of self-play. This is apparently the first application of this algorithm to a complex nontrivial task. It is found that, with zero knowledge built in, the network is able to learn from scratch to play the entire game at a fairly strong intermediate level of performance, which is clearly better than conventional commercial programs, and which in fact surpasses comparable networks trained on a massive human expert data set. The hidden units in these network have apparently discovered useful features, a longstanding goal of computer games research.