Linear programming has been successfully used to compute admissible heuristics for cost-optimal classical planning. Although one of the strengths of linear programming is the ability to express and reason about numeric variables and constraints, their use in numeric planning is limited. In this work, we extend linear programming-based heuristics for classical planning to support numeric state variables. In particular, we propose a model for the interval relaxation, coupled with landmarks and state equation constraints. We consider both linear programming models and their harder-to-solve, yet more informative, integer programming versions. Our experimental analysis shows that considering an NP-Hard heuristic often pays off and that A* search using our integer programming heuristics establishes a new state of the art in cost-optimal numeric planning.

The visual fog paradigm envisions tens of thousands of heterogeneous, camera-enabled edge devices distributed across the Internet, providing live sensing for a myriad of different visual processing applications. The scale, computational demands, and bandwidth needed for visual computing pipelines necessitates offloading intelligently to distributed computing infrastructure, including the cloud, Internet gateway devices, and the edge devices themselves. This paper focuses on the visual fog scheduling problem of assigning the visual computing tasks to various devices to optimize network utilization. We first prove this problem is NP-complete, and then formulate a practical, efficient solution. We demonstrate sub-minute computation time to optimally schedule 20,000 tasks across over 7,000 devices, and just 7-minute execution time to place 60,000 tasks across 20,000 devices, showing our approach is ready to meet the scale challenges introduced by visual fog.

With the rapid growth of microblogging services, such as Twitter, a vast of short and noisy messages are produced by millions of users, which makes people difficult to quickly grasp essential information of their interested topics. In this paper, we study extractive topic-oriented Twitter summarization as a solution to address this problem. Traditional summarization methods only consider text information, which is insufficient in social media situation. Existing Twitter summarization techniques rarely explore relations between tweets explicitly, ignoring that information can spread along the social network. Inspired by social theories that expression consistence and expression contagion are observed in social network, we propose a novel approach for Twitter summarization in short and noisy situation by integrating Social Network and Sparse Reconstruction (SNSR). We explore whether social relations can help Twitter summarization, modeling relations between tweets described as the social regularization and integrating it into the group sparse optimization framework. It conducts a sparse reconstruction process by selecting tweets that can best reconstruct the original tweets in a specific topic, with considering coverage and sparsity. We simultaneously design the diversity regularization to remove redundancy. In particular, we present a mathematical optimization formulation and develop an efficient algorithm to solve it. Due to the lack of public corpus, we construct the gold standard twitter summary datasets for 12 different topics. Experimental results on this datasets show the effectiveness of our framework for handling the large scale short and noisy messages in social media.

The market for selling reusable products (e.g., car rental, cloud services and network access resources) is growing rapidly over the last few years, where service providers maximize their revenues through setting optimal prices. While there has been lots of research on pricing optimization, existing works often ignore dynamic property of demand and the competition among providers. Thus, existing pricing solutions might be far from optimal in realistic markets. This paper provides the first study of service providers' dynamic pricing in consideration of market competition and makes three key contributions along this line. First, we propose a comprehensive model that takes into account the dynamic demand and interaction among providers, and formulate the optimal pricing policy in the competitive market as an equilibrium. Second, we propose an approximate Nash equilibrium to describe providers' behaviors, and design an efficient algorithm to compute the equilibrium which is guaranteed to converge. Third, we derive many properties of the model without any further constraints on demand functions, which can reduce the search space of policies in the algorithm. Finally, we conduct extensive experiments with different parameter settings, showing that the approximate equilibrium is very close to the Nash equilibrium and our proposed pricing policy outperforms existing strategies.

As an important population-based algorithm, ant colony optimization (ACO) has been successfully applied into various combinatorial optimization problems. However, much existing work in ACO focuses on solving centralized problems. In this paper, we present a novel algorithm that takes the power of ants to solve Distributed Constraint Optimization Problems (DCOPs), called ACO_DCOP. In ACO_DCOP, a new mechanism that captures local benefits is proposed to compute heuristic factors and a new method that considers the cost structure of DCOPs is proposed to compute pheromone deltas appropriately. Moreover, pipelining technique is introduced to make full use of the computational capacity and improve the efficiency. In our theoretical analysis, we prove that ACO_DCOP is an anytime algorithm. Our empirical evaluation indicates that ACO_DCOP is able to find solutions of equal or significantly higher quality than state-of-the-art DCOP algorithms.

Recently, binary hashing has been widely applied to data compression, ranking and nearest-neighbor search. Although some promising results have been achieved, effectively optimizing sign function related objectives is still highly challenging and thus pseudo-labels are inevitably used. In this paper, we propose a novel general framework to simultaneously minimize the measurement distortion and the quantization loss, which enable to learn hash functions directly without requiring the pseudo-labels. More significantly, a novel W-Shape Loss (WSL) is specifically developed for hashing so that both the two separate steps of relaxation and the NP-hard discrete optimization are successfully discarded. The experimental results demonstrate that the retrieval performance both in uni-modal and cross-modal settings can be improved.

Open-source indicators such as social media can be very effective precursors for forecasting future societal events. As events are often preceded by social indicators generated by groups of people speaking many different languages, multiple languages need to be considered to ensure comprehensive event forecasting. However, this leads to several technical challenges for traditional models: 1) high dimension, sparsity, and redundancy of features; 2) translation correlation among the multilingual features. and 3) lack of language-wise supervision. In order to simultaneously address these issues, we present a novel model capable of distant-supervision of heterogeneous multitask learning (DHML) for multilingual spatial social event forecasting. This model maps the multilingual heterogeneous features into several latent semantic spaces and then enforces a similar sparsity pattern across them all, using distant supervision across all the languages involved. Optimizing this model creates a difficult problem that is nonconvex and nonsmooth that can then be decomposed into simpler subproblems using the Alternative Direction Multiplier of Methods (ADMM). A novel dynamic programming-based algorithm is proposed to solve one challenging subproblem efficiently. Theoretical properties of the proposed algorithm are analyzed. The results of extensive experiments on multiple real-world datasets are presented to demonstrate the effectiveness, efficiency, and interpretability of the proposed approach.

Earth Mover's Distance (EMD), targeting at measuring the many-to-many distances, has shown its superiority and been widely applied in computer vision tasks, such as object recognition, hyperspectral image classification and gesture recognition. However, there is still little effort concentrated on optimizing the EMD metric towards better matching performance. To tackle this issue, we propose an EMD metric learning algorithm in this paper. In our method, the objective is to learn a discriminative distance metric for EMD ground distance matrix generation which can better measure the similarity between compared subjects. More specifically, given a group of labeled data from different categories, we first select a subset of training data and then optimize the metric for ground distance matrix generation. Here, both the EMD metric and the EMD flow-network are alternatively optimized until a steady EMD value can be achieved. This method is able to generate a discriminative ground distance matrix which can further improve the EMD distance measurement. We then apply our EMD metric learning method on two tasks, i.e., multi-view object classification and document classification. The experimental results have shown better performance of our proposed EMD metric learning method compared with the traditional EMD method and the state-of-the-art methods. It is noted that the proposed EMD metric learning method can be also used in other applications.

Training set bugs are flaws in the data that adversely affect machine learning. The training set is usually too large for manual inspection, but one may have the resources to verify a few trusted items. The set of trusted items may not by itself be adequate for learning, so we propose an algorithm that uses these items to identify bugs in the training set and thus improves learning. Specifically, our approach seeks the smallest set of changes to the training set labels such that the model learned from this corrected training set predicts labels of the trusted items correctly. We flag the items whose labels are changed as potential bugs, whose labels can be checked for veracity by human experts. To find the bugs in this way is a challenging combinatorial bilevel optimization problem, but it can be relaxed into a continuous optimization problem.Experiments on toy and real data demonstrate that our approach can identify training set bugs effectively and suggest appropriate changes to the labels. Our algorithm is a step toward trustworthy machine learning.

This paper addresses the hyperlink prediction problem in hypernetworks. Different from the traditional link prediction problem where only pairwise relations are considered as links, our task here is to predict the linkage of multiple nodes, i.e., hyperlink. Each hyperlink is a set of an arbitrary number of nodes which together form a multiway relationship. Hyperlink prediction is challenging---since the cardinality of a hyperlink is variable, existing classifiers based on a fixed number of input features become infeasible. Heuristic methods, such as the common neighbors and Katz index, do not work for hyperlink prediction, since they are restricted to pairwise similarities. In this paper, we formally define the hyperlink prediction problem, and propose a new algorithm called Coordinated Matrix Minimization (CMM), which alternately performs nonnegative matrix factorization and least square matching in the vertex adjacency space of the hypernetwork, in order to infer a subset of candidate hyperlinks that are most suitable to fill the training hypernetwork. We evaluate CMM on two novel tasks: predicting recipes of Chinese food, and finding missing reactions of metabolic networks. Experimental results demonstrate the superior performance of our method over many seemingly promising baselines.