In the first part of this paper a global Kushner-Clark theorem about the convergence of stochastic algorithms is proved: we show that, under some natural assumptions, one can 'read' from the trajectories of it...
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In the first part of this paper a global Kushner-Clark theorem about the convergence of stochastic algorithms is proved: we show that, under some natural assumptions, one can 'read' from the trajectories of its ODE whether or not an algorithm converges. The classical stochastic optimization results are included in this theorem. In the second part, the above smoothness assumption on the mean vector field of the algorithm is relaxed using a new approach based on a path-dependent Lyapounov functional. Several applications, for non-smooth mean vector fields and/or bounded Lyapounov function settings, are derived. Examples and simulations are provided that illustrate and enlighten the field of application of the theoretical results.
A unified evaluation framework for stochastic tools is developed in this paper. Firstly, we provide a set of already existing quantitative and qualitative metrics that rate the relevant aspects of the performance of a...
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A unified evaluation framework for stochastic tools is developed in this paper. Firstly, we provide a set of already existing quantitative and qualitative metrics that rate the relevant aspects of the performance of a stochastic prognosis algorithm. Secondly, we provide innovative guidelines to detect and minimize the effect of side aspects that interact on the algorithms' performance. Those aspects are related with the input uncertainty (the uncertainty on the data and the prior knowledge), the parametrization method and the uncertainty propagation method. The proposed evaluation framework is contextualized on a Lithium-ion battery Remaining Useful Life prognosis problem. As an example, a Particle Filter is evaluated. On this example, two different data sets taken from NCA aged batteries and two semi-empirical aging models available in the literature fed up the Particle Filter under evaluation. The obtained results show that the proposed framework gives enough details to take decisions about the viability of the chosen algorithm.
The EM algorithm is a widely applicable approach for computing maximum likelihood estimates for incomplete data. We present a stochastic approximation type EM algorithm: SAEM. This algorithm is an adaptation of the st...
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The EM algorithm is a widely applicable approach for computing maximum likelihood estimates for incomplete data. We present a stochastic approximation type EM algorithm: SAEM. This algorithm is an adaptation of the stochastic EM algorithm (SEM) that we have previously developed. Like SEM, SAEM overcomes most of the well-known limitations of EM. Moreover, SAEM performs better for small samples. Furthermore, SAEM appears to be more tractable than SEM, since it provides almost sure convergence, while SEM provides convergence in distribution. Here, we restrict attention on the mixture problem. We state a theorem which asserts that each SAEM sequence converges a.s. to a local maximizer of the likelihood function. We close this paper with a comparative study, based on numerical simulations, of these three algorithms.
Smart grids integrate information technologies to enhance the management of renewable energy sources as well as managing the energy balance between production and consumption. Their design relies on efficiently contro...
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We present a general method how to prove convergence of a sequence of random variables generated by a nonautonomous scheme of the form X-t = T-t(Xt-1, Y-t), where Y-t represents randomness, used as an approximation of...
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We present a general method how to prove convergence of a sequence of random variables generated by a nonautonomous scheme of the form X-t = T-t(Xt-1, Y-t), where Y-t represents randomness, used as an approximation of the set of solutions of the global optimization problem with a continuous cost function. We show some of its applications.
A novel stochastic algorithm using pre-processing technique is proposed in this paper to deal with the problem of underwater target tracking using passive Sonar. Pre-processing is a concept of reducing the variance of...
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A novel stochastic algorithm using pre-processing technique is proposed in this paper to deal with the problem of underwater target tracking using passive Sonar. Pre-processing is a concept of reducing the variance of noise present in the measurements given by sensors. This key step is performed ahead of conventional estimation algorithms. Pre-processed measurements are obtained by taking weighted average of present measurements and projected previous measurements. The method is expected to bring down the variance of noise to a great deal based on the fact that the sensor errors are unbiased by nature. The most attractive feature of this algorithm is the capability to track long range targets in heavy noise environments. The algorithm is tested by running Monte Carlo simulations in Matlab R2009a environment. There, it is shown that the estimation error and the time of convergence of the pre-processing technique based algorithms like pre-processed Unscented Kalman Filter (PP-UKF) and Integrated Unscented Kalman filter (PP-IUKF) are much less compared to their non-pre-processing counterparts namely UKF and IUKF, thus indicating the importance of the proposed novel method. (C) 2016 Elsevier GmbH. All rights reserved.
stochastic optimization has experienced significant growth in recent decades, with the increasing prevalence of variance reduction techniques in stochastic optimization algorithms to enhance computational efficiency. ...
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stochastic optimization has experienced significant growth in recent decades, with the increasing prevalence of variance reduction techniques in stochastic optimization algorithms to enhance computational efficiency. In this paper, we introduce two projection-free stochastic approximation algorithms for maximizing diminishing return (DR) submodular functions over convex constraints, building upon the stochastic Path Integrated Differential EstimatoR (SPIDER) and its variants. Firstly, we present a SPIDER Continuous Greedy (SPIDER-CG) algorithm for the monotone case that guarantees a (1- e(-1))OPT- epsilon approximation after O(epsilon(-1)) iterations and O(epsilon(-2)) stochastic gradient computations under the mean-squared smoothness assumption. For the non-monotone case, we develop a SPIDER Frank-Wolfe (SPIDER-FW) algorithm that guarantees a 1/4 (1- minx (x is an element of C)||x||(infinity))OPT- epsilon approximation withO(epsilon(-1)) iterations and O(epsilon (-2)) stochastic gradient estimates. To address the practical challenge associated with a large number of samples per iteration, we introduce a modified gradient estimator based on SPIDER, leading to a Hybrid SPIDER-FW (Hybrid SPIDER-CG) algorithm, which achieves the same approximation guarantee as SPIDER-FW (SPIDER-CG) algorithm with only O(1) samples per iteration. Numerical experiments on both simulated and real data demonstrate the efficiency of the proposed methods.
In this paper, we propose a novel optimization algorithm for examination timetabling. It works by alternating two phases;one based on a stochastic local search and the other on a deterministic local search. The stocha...
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In this paper, we propose a novel optimization algorithm for examination timetabling. It works by alternating two phases;one based on a stochastic local search and the other on a deterministic local search. The stochastic phase is fundamentally based on biased random sampling that iteratively constructs schedules according to a matrix whose entries are the probability with which exams can be assigned to time slots. The deterministic phase, instead, consists of assigning (according to a given ordering) each exam sequentially to the time slot that causes the lowest increase in the. schedule penalty. After a schedule is constructed, swap operations are executed to improve performance. These two phases are coupled and made closely interactive by tunnelling information on what has happened during one phase to the successive ones. Moreover, the length of a phase and the parameter framework to be used in a new phase are automatically determined by a record of the process. We tested the proposed technique on known benchmarks, and a comparison with 17 algorithms drawn from the state of the art appears to show that our algorithm is able to improve best-known results. In particular, in reference to uncapacitated problems, i.e., the ones without room constraints, our algorithm bested the state of the art in 70% to 90% of the tested instances, while in capacitated problems with overnight conflicts (second-order conflicts), it was superior to all the other algorithms.
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