Portfolio Methods in Uncertain Contexts
Méthodes de portefeuille en contexte incertain
Résumé
This manuscript concentrates in studying methods to handle the noise, including using resampling methods to improve the convergence rates and applying portfolio methods to cases with uncertainties (games, and noisy optimization in continuous domains).Part I will introduce the manuscript, then review the state of the art in noisy optimization, portfolio algorithm, multi-armed bandit algorithms and games.Part II concentrates on the work on noisy optimization:∙ Chapter 4 provides a generic algorithm for noisy optimization recovering most of the existing bounds in one single noisy optimization algorithm.∙ Chapter5 applies different resampling rules in evolution strategies for noisy optimization, without the assumption of variance vanishing in the neighborhood of the optimum, and shows mathematically log-log convergence results and studies experimentally the slope of this convergence.∙ Chapter 6 compares resampling rules used in the differential evolution algorithm for strongly noisy optimization. By mathematical analysis, a new rule is designed for choosing the number of resamplings, as a function of the dimension, and validate its efficiency compared to existing heuristics - though there is no clear improvement over other empirically derived rules.∙ Chapter 7 applies “common random numbers”, also known as pairing, to an intermediate case between black-box and white-box cases for improving the convergence.Part III is devoted to portfolio in adversarial problems:∙ Nash equilibria are cases in which combining pure strategies is necessary for designing optimal strategies. Two chapters are dedicated to the computation of Nash equilibria:– Chapter 9 investigates combinations of pure strategies, when a small set of pure strategies is concerned; basically, we get improved rates when the support of the Nash equilibrium is small.– Chapter 10 applies these results to a power system problem. This compares several bandit algorithms for Nash equilibria, defines parameter-free bandit algorithms, and shows the relevance of the sparsity approach dis- cussed in Chapter 9.∙ Then, two chapters are dedicated to portfolios of game methods:– Chapter 11 shows how to generate multiple policies, from a single one, when only one such policy is available. This kind of bootstrap (based on random seeds) generates many deterministic policies, and then combines them into one better policy. This has been tested on several games.– Chapter 12 extends chapter 11 by combining policies in a position-specific manner. In particular, we get a better asymptotic behavior than MCTS.Part IV is devoted to portfolios in noisy optimization:∙ Chapter 14 is devoted to portfolio of noisy optimization methods in continuous domains;∙ Chapter 15 proposed differential evolution as a tool for non- stationary bandit problems.
Les problèmes d’investissements d’énergie sont difficiles à cause des incertitudes. Certaines incertitudes peuvent être modélisées par les probabilités. Mais il y a des problèmes difficiles tels que l'évolution de technologie et la pénalisation de CO2, délicats à modéliser par des probabilités. Aussi, les travaux sur l’optimisation des systèmes d’énergie est souvent déterministe. Cette thèse s’intéresse à appliquer l’optimisation bruitée aux systèmes d’énergie. Cette thèse se concentre sur trois parties principales: les études des méthodes pour gérer le bruit, y compris utiliser des méthodes de ré-échantillonnage pour améliorer la vitesse de convergence; les applications des méthodes de portefeuilles à l’optimisation bruitée dans le continu; les applications des méthodes de portefeuilles aux cas avec incertitudes pour la planification des investissements d’énergie et aux jeux, y compris l’utilisation de l’algorithme de bandit adversarial pour calculer l’équilibre de Nash d'un jeu matriciel à somme nulle et l’utilisation de “sparsity” pour accélérer le calcul de l’équilibre de Nash.
Origine : Version validée par le jury (STAR)
Loading...