Given an over-constrained system, a Maximal Satisfiable Subset (MSS) denotes a maximal set of constraints that are consistent. A Minimal Correction Subset (MCS, or co-MSS) is the complement of an MSS. MSSes/MCSes find a growing range of practical applications, including optimization, configuration and diagnosis. A number of MCS extraction algorithms have been proposed in recent years, enabling very significant performance gains. This paper builds on earlier work and proposes a finer-grained view of the MCS extraction problem, one that reasons in terms of literals instead of clauses. This view is inspired by the relationship between MCSes and backbones of propositional formulas, which is further investigated, and allows for devising a novel algorithm. Also, the paper develops a number of techniques to approximate (weighted partial) MaxSAT by a selective enumeration of MCSes. Empirical results show substantial improvements over the state of the art in MCS extraction and indicate that MCS-based MaxSAT approximation is very effective in practice.

Inverse optimal control (IOC) is a powerful approach for learning robotic controllers from demonstration that estimates a cost function which rationalizes demonstrated control trajectories. Unfortunately, its applicability is difficult in settings where optimal control can only be solved approximately. While local IOC approaches have been shown to successfully learn cost functions in such settings, they rely on the availability of good reference trajectories, which might not be available at test time. We address the problem of using IOC in these computationally challenging control tasks by using a graph-based discretization of the trajectory space. Our approach projects continuous demonstrations onto this discrete graph, where a cost function can be tractably learned via IOC. Discrete control trajectories from the graph are then projected back to the original space and locally optimized using the learned cost function. We demonstrate the effectiveness of the approach with experiments conducted on two 7-degree of freedom robotic arms.

Abstractive summarization is an ideal form of summarization since it can synthesize information from multiple documents to create concise informative summaries. In this work, we aim at developing an abstractive summarizer. First, our proposed approach identifies the most important document in the multi-document set. The sentences in the most important document are aligned to sentences in other documents to generate clusters of similar sentences. Second, we generate K-shortest paths from the sentences in each cluster using a word-graph structure. Finally, we select sentences from the set of shortest paths generated from all the clusters employing a novel integer linear programming (ILP) model with the objective of maximizing information content and readability of the final summary. Our ILP model represents the shortest paths as binary variables and considers the length of the path, information score and linguistic quality score in the objective function. Experimental results on the DUC 2004 and 2005 multi-document summarization datasets show that our proposed approach outperforms all the baselines and state-of-the-art extractive summarizers as measured by the ROUGE scores. Our method also outperforms a recent abstractive summarization technique. In manual evaluation, our approach also achieves promising results on informativeness and readability.

Many robotic tasks require solutions that maximize multiple performance objectives. For example, in path-planning, these objectives often include finding short paths that avoid risk and maximize the information obtained by the robot. Although there exist many algorithms for multiobjective optimization, few of these algorithms apply directly to robotic path-planning and fewer still are capable of finding the set of Pareto optimal solutions. We present the MORRF*(Multi-Objective Rapidly exploring Random Forest*) algorithm, which blends concepts from two different types of algorithms from the literature: Optimal rapidly exploring random tree (RRT*) for efficient path finding and a decomposition-based approach to multi-objective optimization. The random forest uses two types of tree structures: a set of reference trees and a set of subproblem trees. We present a theoretical analysis that demonstrates that the algorithm asymptotically produces the set of Pareto optimal solutions, and use simulations to demonstrate the effectiveness and efficiency of MORRF* in approximating the Pareto set.

In this paper, we formulate a sparse optimization framework for extractive document summarization. The proposed framework has a decomposable convex objective function. We derive an efficient ADMM algorithm to solve it. To encourage diversity in the summaries, we explicitly introduce an additional sentence dissimilarity term in the optimization framework. We achieve significant improvement over previous related work under similar data reconstruction framework. We then generalize our formulation to the case of compressive summarization and derive a block coordinate descent algorithm to optimize the objective function. Performance on DUC 2006 and DUC 2007 datasets shows that our compressive summarization results are competitive against the state-of-the-art results while maintaining reasonable readability.

Knowledge bases (KBs) are often greatly incomplete, necessitating a demand for KB completion. A promising approach is to embed KBs into latent spaces and make inferences by learning and operating on latent representations. Such embedding models, however, do not make use of any rules during inference and hence have limited accuracy. This paper proposes a novel approach which incorporates rules seamlessly into embedding models for KB completion. It formulates inference as an integer linear programming (ILP) problem, with the objective function generated from embedding models and the constraints translated from rules. Solving the ILP problem results in a number of facts which 1) are the most preferred by the embedding models, and 2) comply with all the rules. By incorporating rules, our approach can greatly reduce the solution space and significantly improve the inference accuracy of embedding models. We further provide a slacking technique to handle noise in KBs, by explicitly modeling the noise with slack variables. Experimental results on two publicly available data sets show that our approach significantly and consistently outperforms state-of-the-art embedding models in KB completion. Moreover, the slacking technique is effective in identifying erroneous facts and ambiguous entities, with a precision higher than 90%.

Interactive gender inference aims to infer the genders of the two involved users in a communication from the interactive text. In this paper, we address this task by proposing a joint inference approach which well incorporates label correlations among the instances. Specifically, an Integer Linear Programming (ILP) approach is proposed to achieve global optimization with various kinds of intra-task and extra-task constraints. Empirical studies demonstrate the effectiveness of the proposed ILP-based approach to interactive gender inference.

Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex techniques to find only local optima, even with extensions like random restarts and simulated annealing. We observe that, in many cases, the local modes of the objective function have combinatorial structure, and thus ideas from combinatorial optimization can be brought to bear. Based on this, we propose a problem-decomposition approach to nonconvex optimization. Similarly to DPLL-style SAT solvers and recursive conditioning in probabilistic inference, our algorithm, RDIS, recursively sets variables so as to simplify and decompose the objective function into approximately independent sub-functions, until the remaining functions are simple enough to be optimized by standard techniques like gradient descent. The variables to set are chosen by graph partitioning, ensuring decomposition whenever possible. We show analytically that RDIS can solve a broad class of nonconvex optimization problems exponentially faster than gradient descent with random restarts. Experimentally, RDIS outperforms standard techniques on problems like structure from motion and protein folding.

Social networks, due to their popularity, have been studied extensively these years. A rich body of these studies is related to influence maximization, which aims to select a set of seed nodes for maximizing the expected number of active nodes at the end of the process. However, the set of active nodes can not fully represent the true coverage of information propagation. A node may be informed of the information when any of its neighbours become active and try to activate it, though this node (namely informed node) is still inactive. Therefore, we need to consider both active nodes and informed nodes that are aware of the information when we study the coverage of information propagation in a network. Along this line, in this paper we propose a new problem called Information Coverage Maximization that aims to maximize the expected number of both active nodes and informed ones. After we prove that this problem is NP-hard and submodular in the independent cascade model, we design two algorithms to solve it. Extensive experiments on three real-world data sets demonstrate the performance of the proposed algorithms.

This paper addresses two classes of different, yet interrelated optimization problems. The first class of problems involves a robot that must locate a hidden target in an environment that consists of a set of concurrent rays. The second class pertains to the design of interruptible algorithms by means of a schedule of contract algorithms. We study several variants of these families of problems, such as searching and scheduling with probabilistic considerations, redundancy and fault-tolerance issues, randomized strategies, and trade-offs between performance and preemptions. For many of these problems we present the first known results that apply to multi-ray and multi-problem domains. Our objective is to demonstrate that several well-motivated settings can be addressed using a common approach.