We consider online planning in Markov decision processes (MDPs). In online planning, the agent focuses on its current state only, deliberates about the set of possible policies from that state onwards and, when interrupted, uses the outcome of that exploratory deliberation to choose what action to perform next. The performance of algorithms for online planning is assessed in terms of simple regret, which is the agent's expected performance loss when the chosen action, rather than an optimal one, is followed. To date, state-of-the-art algorithms for online planning in general MDPs are either best effort, or guarantee only polynomial-rate reduction of simple regret over time. Here we introduce a new Monte-Carlo tree search algorithm, BRUE, that guarantees exponential-rate reduction of simple regret and error probability. This algorithm is based on a simple yet non-standard state-space sampling scheme, MCTS2e, in which different parts of each sample are dedicated to different exploratory objectives. Our empirical evaluation shows that BRUE not only provides superior performance guarantees, but is also very effective in practice and favorably compares to state-of-the-art. We then extend BRUE with a variant of "learning by forgetting." The resulting set of algorithms, BRUE(alpha), generalizes BRUE, improves the exponential factor in the upper bound on its reduction rate, and exhibits even more attractive empirical performance.

"Information processing" is a not-so-long-ago launched buzzword that is extensively used in many research fields and communities. Despite of its widespread popularity, the real meaning of it is far less acknowledged and understood. Wikipedia [1] and Plato (Stanford Encyclopedia of Philosophy) [2] provide special entries for it, but even in the lightest manner, these entries do not confront the threatening ambiguity and incomprehensibility of this expression. Positing that "Information processing is the change (processing) of information "[1] in any way does not clarify its elusive essence. The reason for that is simple - the key component of the expression ("information") has never been defined and never determined, neither in the times of ancient philosophers nor in these glorious days, when "information era" has become our blossoming reality. It is worth to be mentioned - even today "information" does not have an accepted and a generally agreed definition. Far worse than that - it has always been (and continues to be) a "bone of contention" between many prominent thinkers, scholars and scientists. I do not intend to take part in this controversy. In the paper's Reference section I provide a list of some relevant publications addressing this issue, with only one and a definite purpose in mind - to give the vigilant readers a fair opportunity to verify by themselves how useful and applicable are the concepts of information that these leading thinkers and scholars are developing and advance (L.

We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order operations (e.g., certain optimizations) are considered primitive for the purposes of measuring complexity. We consider classes of information operators and algorithms made up of scaled families, and investigate the utility of scaling the complexities to minimize error. We look at the division of statistical learning into information and algorithmic components, at the complexities of each, and at applications to support vector machine (SVM) and more general machine learning algorithms. We give applications to SVM algorithms graded into linear and higher order components, and give an example in biomedical informatics.

We propose a generative model of a group EEG analysis, based on appropriate kernel assumptions on EEG data. We derive the variational inference update rule using various approximation techniques. The proposed model outperforms the current state-of-the-art algorithms in terms of common pattern extraction. The validity of the proposed model is tested on the BCI competition dataset.

We propose a probabilistic model for the parallel execution of Las Vegas algorithms, i.e., randomized algorithms whose runtime might vary from one execution to another, even with the same input. This model aims at predicting the parallel performances (i.e., speedups) by analysis the runtime distribution of the sequential runs of the algorithm. Then, we study in practice the case of a particular Las Vegas algorithm for combinatorial optimization, on three classical problems, and compare with an actual parallel implementation up to 256 cores. We show that the prediction can be quite accurate, matching the actual speedups very well up to 100 parallel cores and then with a deviation of about 20% up to 256 cores.

A new procedure, called DDa-procedure, is developed to solve the problem of classifying d-dimensional objects into q >= 2 classes. The procedure is completely nonparametric; it uses q-dimensional depth plots and a very efficient algorithm for discrimination analysis in the depth space [0,1]^q. Specifically, the depth is the zonoid depth, and the algorithm is the alpha-procedure. In case of more than two classes several binary classifications are performed and a majority rule is applied. Special treatments are discussed for 'outsiders', that is, data having zero depth vector. The DDa-classifier is applied to simulated as well as real data, and the results are compared with those of similar procedures that have been recently proposed. In most cases the new procedure has comparable error rates, but is much faster than other classification approaches, including the SVM.

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of nonzero loadings in these combinations. In this paper we consider 8 different optimization formulations for computing a single sparse loading vector; these are obtained by combining the following factors: we employ two norms for measuring variance (L2, L1) and two sparsity-inducing norms (L0, L1), which are used in two different ways (constraint, penalty). Three of our formulations, notably the one with L0 constraint and L1 variance, have not been considered in the literature. We give a unifying reformulation which we propose to solve via a natural alternating maximization (AM) method. We show the the AM method is nontrivially equivalent to GPower (Journ\'{e}e et al; JMLR 11:517--553, 2010) for all our formulations. Besides this, we provide 24 efficient parallel SPCA implementations: 3 codes (multi-core, GPU and cluster) for each of the 8 problems. Parallelism in the methods is aimed at i) speeding up computations (our GPU code can be 100 times faster than an efficient serial code written in C++), ii) obtaining solutions explaining more variance and iii) dealing with big data problems (our cluster code is able to solve a 357 GB problem in about a minute).

Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms and implementations are critical to efficiently solving these problems. Building upon previous work on coordinate descent algorithms for L1-regularized problems, we introduce a novel family of algorithms called block-greedy coordinate descent that includes, as special cases, several existing algorithms such as SCD, Greedy CD, Shotgun, and Thread-Greedy. We give a unified convergence analysis for the family of block-greedy algorithms. The analysis suggests that block-greedy coordinate descent can better exploit parallelism if features are clustered so that the maximum inner product between features in different blocks is small. Our theoretical convergence analysis is supported with experimental re- sults using data from diverse real-world applications. We hope that algorithmic approaches and convergence analysis we provide will not only advance the field, but will also encourage researchers to systematically explore the design space of algorithms for solving large-scale L1-regularization problems.

This paper presents a model based on an hybrid system to numerically simulate the climbing phase of an aircraft. This model is then used within a trajectory prediction tool. Finally, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) optimization algorithm is used to tune five selected parameters, and thus improve the accuracy of the model. Incorporated within a trajectory prediction tool, this model can be used to derive the order of magnitude of the prediction error over time, and thus the domain of validity of the trajectory prediction. A first validation experiment of the proposed model is based on the errors along time for a one-time trajectory prediction at the take off of the flight with respect to the default values of the theoretical BADA model. This experiment, assuming complete information, also shows the limit of the model. A second experiment part presents an on-line trajectory prediction, in which the prediction is continuously updated based on the current aircraft position. This approach raises several issues, for which improvements of the basic model are proposed, and the resulting trajectory prediction tool shows statistically significantly more accurate results than those of the default model.

Nowadays, huge efforts are made to modernize the air traffic management systems to cope with uncertainty, complexity and sub-optimality. An answer is to enhance the information sharing between the stakeholders. This paper introduces a framework that bridges the gap between air traffic management and air traffic control on the one hand, and bridges the gap between the ground, the approach and the en-route centers on the other hand. An original system is presented, that has three essential components: the trajectory models, the optimization process, and the monitoring process. The uncertainty of the trajectory is modeled with a Bayesian Network, where the nodes are associated to two types of random variables: the time of overflight on metering points of the airspace, and the traveling time of the routes linking these points. The resulting Bayesian Network covers the complete airspace, and Monte- Carlo simulations are done to estimate the probabilities of sector congestion and delays. On top of this trajectory model, an optimization process minimizes these probabilities by tuning the parameters of the Bayesian trajectory model related to overflight times on metering points. The last component is the monitoring process, that continuously updates the situation of the airspace, modifying the trajectories uncertainties according to actual positions of aircraft. After each update, a new optimal set of overflight times is computed, and can be communicated to the controllers as clearances for the aircraft pilots. The paper presents a formal specification of this global optimization problem, whose underlying rationale was derived with the help of air traffic controllers at Thales Air Systems.