14 research outputs found
Contributions à l'Analyse de Convergence d'Algorithmes d'Optimisation Bruitée
This thesis exposes contributions to the analysis of algorithms for noisy functions. It exposes convergence rates for linesearch algorithms as well as for random search algorithms. We prove in terms of Simple Regret and Cumulative Regret that a Hessian based algorithm can reach the same results as some optimal algorithms in the literature, when parameters are tuned correctly. On the other hand we analyse the convergence order of Evolution Strategies when solving noisy functions. We deduce log-log convergence. We also give a lower bound for the convergence rate of the Evolution Strategies. We extend the work on revaluation by applying it to a discrete settings. Finally we analyse the performance measure itself and prove that the use of an erroneus performance measure can lead to misleading results on the evaluation of different methods.Cette thèse montre des contributions à l'analyse d'algorithmes pour l'optimisation de fonctions bruitées. Les taux de convergences (regret simple et regret cumulatif) sont analysés pour les algorithmes de recherche linéaire ainsi que pour les algorithmes de recherche aléatoires. Nous prouvons que les algorithmes basé sur la matrice hessienne peuvent atteindre le même résultat que certaines algorithmes optimaux, lorsque les paramètres sont bien choisis. De plus, nous analysons l'ordre de convergence des stratégies évolutionnistes pour des fonctions bruitées. Nous déduisons une convergence log-log. Nous prouvons aussi une borne basse pour le taux de convergence de stratégies évolutionnistes. Nous étendons le travail effectué sur les mécanismes de réévaluations en les appliquant au cas discret. Finalement, nous analysons la mesure de performance en elle-même et prouvons que l'utilisation d'une mauvaise mesure de performance peut mener à des résultats trompeurs lorsque différentes méthodes d'optimisation sont évaluées
Desarrollo de indices de temor al crimen y sus factores influyentes relevantes
Ingeniera Civil MatemáticaEsta memoria tiene como objetivo la construcción de uno o más índices de temor al crimen, además del análisis de la influencia de variables sociodemográficas y de victimi- zación sobre éste o estos índices.
El temor al crimen es un concepto desarrollado por criminólogos internacionales durante el siglo XX. La subjetividad de la definición del temor al crimen y la multidimensionalidad que presenta lo hacen difícil de medir.
En esta memoria de título se explora la posibilidad de obtener índices que contengan la mayor cantidad de información posible respecto a la percepción de inseguridad de los individuos. Para esto, se intenta representar variados aspectos del temor al crimen, todos ellos introducidos por expertos. Estos aspectos corresponden a niveles de temor afectivo, cognitivo, de comportamiento y de percepción. Y engloban varias aristas, tales como reac- ciones instintivas, acciones que los individuos realizan para evitar los delitos y percepciones sociales.
Para la medición de estos aspectos del temor al crimen se analizan las bases de datos de la Encuesta Nacional Urbana de Seguridad Ciudadana, realizada anualmente en Chile, la cual es representativa a nivel país y contiene una sección completa de Percepción y reac- ción frente al delito. Las variables medidas en esta sección son seleccionadas dependiendo de su competencia en cada aspecto del temor al crimen. A partir de esta selección se aplican desarrollan tres métodos estadísticos para la obtención de los índices: CATPCA, SEM y clasificación de grupos. Se obtienen resultados consistentes para los cuatro años considerados (2008, 2009, 2010, 2011).
Para el análisis descriptivo de los índices obtenidos, observando la influencia de factores sociodemográficos y de victimización, se utilizan Regresiones Lineales, Test χ2 y Modelos Mixtos.
Sostenidamente, considerando los diferentes índices obtenidos y los métodos descripti- vos utilizados, se hallan las variables de Nivel Socioeconómico y algunas variables de victimización (como Victimización General o Robo en el hogar) como las más relevantes dentro del análisis
Analysis of runtime of optimization algorithms for noisy functions over discrete codomains
International audienceWe consider in this work the application of optimization algorithms to problems over discrete codomains corrupted by additive unbiased noise. We propose a modification of the algorithms by repeating the fitness evaluation of the noisy function sufficiently so that, with a fix probability, the function evaluation on the noisy case is identical to the true value. If the runtime of the algorithms on the noise-free case is known, the number of resampling is chosen accordingly. If not, the number of resampling is chosen regarding to the number of fitness evaluations, in an anytime manner. We conclude that if the additive noise is Gaussian, then the runtime on the noisy case, for an adapted algorithm using resamplings, is similar to the runtime on the noise-free case: we incur only an extra logarithmic factor. If the noise is non-Gaussian but with finite variance, then the total runtime of the noisy case is quadratic in function of the runtime on the noise-free case
Evolution Strategies with Additive Noise: A Convergence Rate Lower Bound
International audienceWe consider the problem of optimizing functions corrupted with additive noise. It is known that evolutionary algo-rithms can reach a simple regret O(1/ √ n) within logarith-mic factors, when n is the number of function evaluations. We show mathematically that this bound is tight, at least for a wide family of evolution strategies without large mutations
Log-log Convergence for Noisy Optimization
International audienceWe consider noisy optimization problems, without the as-sumption of variance vanishing in the neighborhood of the optimum. We show mathematically that simple rules with exponential number of re-samplings lead to a log-log convergence rate. In particular, in this case the log of the distance to the optimum is linear on the log of the num-ber of resamplings. As well as with number of resamplings polynomial in the inverse step-size. We show empirically that this convergence rate is obtained also with polynomial number of resamplings. In this polyno-mial resampling setting, using classical evolution strategies and an ad hoc choice of the number of resamplings, we seemingly get the same rate as those obtained with specific Estimation of Distribution Algorithms de-signed for noisy setting. We also experiment non-adaptive polynomial re-samplings. Compared to the state of the art, our results provide (i) proofs of log-log convergence for evolution strategies (which were not covered by existing results) in the case of objective functions with quadratic expec-tations and constant noise, (ii) log-log rates also for objective functions with expectation E[f (x)] = ||x − x * || p , where x * represents the optimum (iii) experiments with different parametrizations than those considered in the proof. These results propose some simple revaluation schemes. This paper extends [1]
Criteria and Convergence Rates in Noisy Optimization
International audienceIn an optimization framework, some criteria might be more relevant than others; the internal computational cost of the optimization algorithm might be negligible or not; the quality of intermediate search points might be important or not. For this reason measuring the performance of an algorithm is a delicate task. In addition, the usual criteria are often approximated for the sake of simplicity of the analysis, or for simplifying the design of test beds. This situation makes sense both in noise-free and noisy settings; however it is more often crucial in the latter case. We here discuss and compare several performance criteria published in the literature in the case of noisy optimization. We review existing rates, for various existing criteria, propose new rates, and check if some classically observed criteria are good approximations of sound criteria