This article reports on the first international Competition of Distributed and Multiagent Planners (CoDMAP). The competition focused on cooperative domain-independent planners compatible with a minimal multiagent extension of the classical planning model. The motivations for the competition were manifold: to standardize the problem description language with a common set of benchmarks, to promote development of multiagent planners both inside and outside of the multiagent research community, and to serve as a prototype for future multiagent planning competitions. The article provides an overview of cooperative multiagent planning, describes a novel variant of standardized input language for encoding mutliagent planning problems and summarizes the key points of organization, competing planners and results of the competition.

In addition, we illustrate the potential of ASP including molecular biology (Gebser et computational hardness of our application problem al. 2010a, 2010b), decision support system for space by explaining its connection to the NPcomplete shuttle controllers (Balduccini, Gelfond, and decision problem Exact-3-SAT.

Its main ideas are described in the article by Janhunen and Niemelä (2016) and in other contributions to this special issue. In this introductory article my goal is to discuss the concept of an answer set, or stable model, which defines the semantics of ASP languages. The answer sets of a logic program are sets of atomic formulas without variables ("ground atoms"), and they were introduced in the course of research on the semantics of negation in Prolog. For this reason, I will start with examples illustrating the relationship between answer sets and Prolog and the relationship between answer set solvers and Prolog systems. Then I will review the mathematical definition of an answer set and discuss some extensions of the basic language of ASP.

What distinguishes ASP from other declarative paradigms, like satisfiability (SAT) or constraint solving (CSP), is its underlying modeling language and the semantics involved. Problems are specified using logic programminglike rules, with some convenient extensions facilitating compact and readable problem descriptions. Sets of such rules, or answer set programs, come with an intuitive, well-defined and, by now, well-accepted semantics. This semantics has its roots in research in knowledge representation, in particular nonmonotonic reasoning, and avoids the pitfalls of earlier attempts such as the procedural semantics of Prolog based on negation as finite failure. This semantics was originally called the stable-model semantics and was defined for normal logic programs only, that is, programs consisting of rules with a single atom in the head and any finite number of atoms, possibly preceded by default negation, not, in the body. Stable models were later generalized to broader classes of programs, where the semantics can no longer be defined in terms of sets of atoms, which is a natural representation of classical models. Instead, it was defined by means of some sets of literals. For this reason the term answer set was adopted as more adequate (although answer sets also have a straightforward interpretation as models, albeit three-valued ones). Over the last decade or so, ASP has evolved into a vibrant and active research area that produced not only theoretical insights, but also highly effective and useful software tools and interesting and promising applications.

Nonparametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging indications on the effectiveness of the method. An application to density-based clustering illustrates a possible usage. Consider estimation of the probability density function f(·) of a continuous random variable in cases when a parametric formulation for f is not considered appropriate. Given a random sample drawn form f, a variety of nonparametric estimation methods are available.

Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. To achieve dimensionality reduction, we present a sketching-based approach for rank change detection using the low-dimensional linear sketches of the original high-dimensional observations. The premise is that when the sketching matrix is a random Gaussian matrix, and the dimension of the sketching vector is sufficiently large, the rank of sample covariance matrix for these sketches equals the rank of the original sample covariance matrix with high probability. Hence, we may be able to detect the low-rank change using sample covariance matrices of the sketches without having to recover the original covariance matrix. We character the performance of the largest eigenvalue statistic in terms of the false-alarm-rate and the expected detection delay, and present an efficient online implementation via subspace tracking.

An optimization problem can be called large scale if it involves a large number of optimization variables, and/or a large number of input parameters, and/or a large number of constraints. The increasing availability of distributed hardware suggests to address large scale optimization problems by distributed algorithms. Here we design and analyze a distributed algorithm for general convex optimization problems that involve a large number of constraints. The algorithm is a variant of the alternating direction method of multipliers (ADMM) that was proposed by Glowinski and Marroco [7] and by Gabay and Mercier [4]. Recently, ADMM regained significant attention, especially in the machine learning community, because it allows to solve convex optimization problems that involve a large number of parameters in a distributed setting [2]. In a typical machine learning method, like the least squares method for regression problems, the parameters are just the data points. Hence, ADMM is often the method of choice for Big Data problems, where the data does not fit into the memory of a single compute node. The optimization problem behind a typical Big Data machine learning method usually aims at minimizing a so called loss-function that is the sum of the losses for each data point. Hence, the objective function f of such problems is separable, i.e., it holds that f(x)

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However, the representation is non-standardized, and the gradient calculation methods are often performed using component-based approaches that break parameters down into scalar units, instead of considering the parameters as whole entities. In this work, these problems are addressed. Standard notation is used to represent DNNs in a compact framework. Gradients of DNN loss functions are calculated directly over the inner product space on which the parameters are defined. This framework is general and is applied to two common network types: the Multilayer Perceptron and the Deep Autoencoder.

Feature selection methods are usually evaluated by wrapping specific classifiers and datasets in the evaluation process, resulting very often in unfair comparisons between methods. In this work, we develop a theoretical framework that allows obtaining the true feature ordering of two-dimensional sequential forward feature selection methods based on mutual information, which is independent of entropy or mutual information estimation methods, classifiers, or datasets, and leads to an undoubtful comparison of the methods. Moreover, the theoretical framework unveils problems intrinsic to some methods that are otherwise difficult to detect, namely inconsistencies in the construction of the objective function used to select the candidate features, due to various types of indeterminations and to the possibility of the entropy of continuous random variables taking null and negative values.

We consider the online version of the isotonic regression problem. Given a set of linearly ordered points (e.g., on the real line), the learner must predict labels sequentially at adversarially chosen positions and is evaluated by her total squared loss compared against the best isotonic (non-decreasing) function in hindsight. We survey several standard online learning algorithms and show that none of them achieve the optimal regret exponent; in fact, most of them (including Online Gradient Descent, Follow the Leader and Exponential Weights) incur linear regret. We then prove that the Exponential Weights algorithm played over a covering net of isotonic functions has a regret bounded by $O\big(T^{1/3} \log^{2/3}(T)\big)$ and present a matching $\Omega(T^{1/3})$ lower bound on regret. We provide a computationally efficient version of this algorithm. We also analyze the noise-free case, in which the revealed labels are isotonic, and show that the bound can be improved to $O(\log T)$ or even to $O(1)$ (when the labels are revealed in isotonic order). Finally, we extend the analysis beyond squared loss and give bounds for entropic loss and absolute loss.