Pattern Search Ranking and Selection Algorithms for Mixed-Variable Optimization of Stochastic Systems

A new class of algorithms is introduced and analyzed for bound and linearly constrained optimization problems with stochastic objective functions and a mixture of design variable types. The generalized pattern search (GPS) class of algorithms is extended to a new problem setting in which objective function evaluations require sampling from a model of a stochastic system. The approach combines GPS with ranking and selection (R&S) statistical procedures to select new iterates. The derivative-free algorithms require only black-box simulation responses and are applicable over domains with mixed variables (continuous, discrete numeric, and discrete categorical) to include bound and linear constraints on the continuous variables. A convergence analysis for the general class of algorithms establishes almost sure convergence of an iteration subsequence to stationary points appropriately defined in the mixed-variable domain. Additionally, specific algorithm instances are implemented that provide computational enhancements to the basic algorithm. Implementation alternatives include the use modern R&S procedures designed to provide efficient sampling strategies and the use of surrogate functions that augment the search by approximating the unknown objective function with nonparametric response surfaces. In a computational evaluation, six variants of the algorithm are tested along with four competing methods on 26 standardized test problems. The numerical results validate the use of advanced implementations as a means to improve algorithm performance

Toward Controllable and Robust Surface Reconstruction from Spatial Curves

Reconstructing surface from a set of spatial curves is a fundamental problem in computer graphics and computational geometry. It often arises in many applications across various disciplines, such as industrial prototyping, artistic design and biomedical imaging. While the problem has been widely studied for years, challenges remain for handling different type of curve inputs while satisfying various constraints. We study studied three related computational tasks in this thesis. First, we propose an algorithm for reconstructing multi-labeled material interfaces from cross-sectional curves that allows for explicit topology control. Second, we addressed the consistency restoration, a critical but overlooked problem in applying algorithms of surface reconstruction to real-world cross-sections data. Lastly, we propose the Variational Implicit Point Set Surface which allows us to robustly handle noisy, sparse and non-uniform inputs, such as samples from spatial curves

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

OPTIMIZATION OF ALGORITHMS WITH THE OPAL FRAMEWORK

RÉSUMÉ La question d'identifier de bons paramètres a été étudiée depuis longtemps et on peut compter un grand nombre de recherches qui se concentrent sur ce sujet. Certaines de ces recherches manquent de généralité et surtout de re-utilisabilité. Une première raison est que ces projets visent des systèmes spécifiques. En plus, la plupart de ces projets ne se concentrent pas sur les questions fondamentales de l'identification de bons paramètres. Et enfin, il n'y avait pas un outil puissant capable de surmonter des difficulté dans ce domaine. En conséquence, malgré un grand nombre de projets, les utilisateurs n'ont pas trop de possibilité à appliquer les résultats antérieurs à leurs problèmes. Cette thèse propose le cadre OPAL pour identifier de bons paramètres algorithmiques avec des éléments essentiels, indispensables. Les étapes de l'élaboration du cadre de travail ainsi que les résultats principaux sont présentés dans trois articles correspondant aux trois chapitres 4, 5 et 6 de la thèse. Le premier article introduit le cadre par l'intermédiaire d'exemples fondamentaux. En outre, dans ce cadre, la question d'identifier de bons paramètres est modélisée comme un problème d'optimisation non-lisse qui est ensuite résolu par un algorithme de recherche directe sur treillis adaptatifs. Cela réduit l'effort des utilisateurs pour accomplir la tâche d'identifier de bons paramètres. Le deuxième article décrit une extension visant à améliorer la performance du cadre OPAL. L'utilisation efficace de ressources informatiques dans ce cadre se fait par l'étude de plusieurs stratégies d'utilisation du parallélisme et par l'intermédiaire d'une fonctionnalité particulière appelée l'interruption des tâches inutiles. Le troisième article est une description complète du cadre et de son implémentation en Python. En plus de rappeler les caractéristiques principales présentées dans des travaux antérieurs, l'intégration est présentée comme une nouvelle fonctionnalité par une démonstration de la coopération avec un outil de classification. Plus précisément, le travail illustre une coopération de OPAL et un outil de classification pour résoudre un problème d'optimisation des paramètres dont l'ensemble de problèmes tests est trop grand et une seule évaluation peut prendre une journée.----------ABSTRACT The task of parameter tuning question has been around for a long time, spread over most domains and there have been many attempts to address it. Research on this question often lacks in generality and re-utilisability. A first reason is that these projects aim at specific systems. Moreover, some approaches do not concentrate on the fundamental questions of parameter tuning. And finally, there was not a powerful tool that is able to take over the difficulties in this domain. As a result, the number of projects continues to grow, while users are not able to apply the previous achievements to their own problem. The present work systematically approaches parameter tuning by figuring out the fundamental issues and identifying the basic elements for a general system. This provides the base for developing a general and flexible framework called OPAL, which stands for OPtimization of ALgorithms. The milestones in developing the framework as well as the main achievements are presented through three papers corresponding to the three chapters 4, 5 and 6 of this thesis. The first paper introduces the framework by describing the crucial basic elements through some very simple examples. To this end, the paper considers three questions in constructing an automated parameter tuning framework. By answering these questions, we propose OPAL, consisting of indispensable components of a parameter tuning framework. OPAL models the parameter tuning task as a blackbox optimization problem. This reduces the effort of users in launching a tuning session. The second paper shows one of the opportunities to extend the framework. To take advantage of the situations where multiple processors are available, we study various ways of embedding parallelism and develop a feature called ''interruption of unnecessary tasks'' in order to improve performance of the framework. The third paper is a full description of the framework and a release of its Python} implementation. In addition to the confirmations on the methodology and the main features presented in previous works, the integrability is introduced as a new feature of this release through an example of the cooperation with a classification tool. More specifically, the work illustrates a cooperation of OPAL and a classification tool to solve a parameter optimization problem of which the test problem set is too large and an assessment can take a day

Democratizing machine learning

Modelle des maschinellen Lernens sind zunehmend in der Gesellschaft verankert, oft in Form von automatisierten Entscheidungsprozessen. Ein wesentlicher Grund dafür ist die verbesserte Zugänglichkeit von Daten, aber auch von Toolkits für maschinelles Lernen, die den Zugang zu Methoden des maschinellen Lernens für Nicht-Experten ermöglichen. Diese Arbeit umfasst mehrere Beiträge zur Demokratisierung des Zugangs zum maschinellem Lernen, mit dem Ziel, einem breiterem Publikum Zugang zu diesen Technologien zu er- möglichen. Die Beiträge in diesem Manuskript stammen aus mehreren Bereichen innerhalb dieses weiten Gebiets. Ein großer Teil ist dem Bereich des automatisierten maschinellen Lernens (AutoML) und der Hyperparameter-Optimierung gewidmet, mit dem Ziel, die oft mühsame Aufgabe, ein optimales Vorhersagemodell für einen gegebenen Datensatz zu finden, zu vereinfachen. Dieser Prozess besteht meist darin ein für vom Benutzer vorgegebene Leistungsmetrik(en) optimales Modell zu finden. Oft kann dieser Prozess durch Lernen aus vorhergehenden Experimenten verbessert oder beschleunigt werden. In dieser Arbeit werden drei solcher Methoden vorgestellt, die entweder darauf abzielen, eine feste Menge möglicher Hyperparameterkonfigurationen zu erhalten, die wahrscheinlich gute Lösungen für jeden neuen Datensatz enthalten, oder Eigenschaften der Datensätze zu nutzen, um neue Konfigurationen vorzuschlagen. Darüber hinaus wird eine Sammlung solcher erforderlichen Metadaten zu den Experimenten vorgestellt, und es wird gezeigt, wie solche Metadaten für die Entwicklung und als Testumgebung für neue Hyperparameter- Optimierungsmethoden verwendet werden können. Die weite Verbreitung von ML-Modellen in vielen Bereichen der Gesellschaft erfordert gleichzeitig eine genauere Untersuchung der Art und Weise, wie aus Modellen abgeleitete automatisierte Entscheidungen die Gesellschaft formen, und ob sie möglicherweise Individuen oder einzelne Bevölkerungsgruppen benachteiligen. In dieser Arbeit wird daher ein AutoML-Tool vorgestellt, das es ermöglicht, solche Überlegungen in die Suche nach einem optimalen Modell miteinzubeziehen. Diese Forderung nach Fairness wirft gleichzeitig die Frage auf, ob die Fairness eines Modells zuverlässig geschätzt werden kann, was in einem weiteren Beitrag in dieser Arbeit untersucht wird. Da der Zugang zu Methoden des maschinellen Lernens auch stark vom Zugang zu Software und Toolboxen abhängt, sind mehrere Beiträge in Form von Software Teil dieser Arbeit. Das R-Paket mlr3pipelines ermöglicht die Einbettung von Modellen in sogenan- nte Machine Learning Pipelines, die Vor- und Nachverarbeitungsschritte enthalten, die im maschinellen Lernen und AutoML häufig benötigt werden. Das mlr3fairness R-Paket hingegen ermöglicht es dem Benutzer, Modelle auf potentielle Benachteiligung hin zu über- prüfen und diese durch verschiedene Techniken zu reduzieren. Eine dieser Techniken, multi-calibration wurde darüberhinaus als seperate Software veröffentlicht.Machine learning artifacts are increasingly embedded in society, often in the form of automated decision-making processes. One major reason for this, along with methodological improvements, is the increasing accessibility of data but also machine learning toolkits that enable access to machine learning methodology for non-experts. The core focus of this thesis is exactly this – democratizing access to machine learning in order to enable a wider audience to benefit from its potential. Contributions in this manuscript stem from several different areas within this broader area. A major section is dedicated to the field of automated machine learning (AutoML) with the goal to abstract away the tedious task of obtaining an optimal predictive model for a given dataset. This process mostly consists of finding said optimal model, often through hyperparameter optimization, while the user in turn only selects the appropriate performance metric(s) and validates the resulting models. This process can be improved or sped up by learning from previous experiments. Three such methods one with the goal to obtain a fixed set of possible hyperparameter configurations that likely contain good solutions for any new dataset and two using dataset characteristics to propose new configurations are presented in this thesis. It furthermore presents a collection of required experiment metadata and how such meta-data can be used for the development and as a test bed for new hyperparameter optimization methods. The pervasion of models derived from ML in many aspects of society simultaneously calls for increased scrutiny with respect to how such models shape society and the eventual biases they exhibit. Therefore, this thesis presents an AutoML tool that allows incorporating fairness considerations into the search for an optimal model. This requirement for fairness simultaneously poses the question of whether we can reliably estimate a model’s fairness, which is studied in a further contribution in this thesis. Since access to machine learning methods also heavily depends on access to software and toolboxes, several contributions in the form of software are part of this thesis. The mlr3pipelines R package allows for embedding models in so-called machine learning pipelines that include pre- and postprocessing steps often required in machine learning and AutoML. The mlr3fairness R package on the other hand enables users to audit models for potential biases as well as reduce those biases through different debiasing techniques. One such technique, multi-calibration is published as a separate software package, mcboost