Heteroscedastic metamodeling has gained popularity as an effective tool for analyzing and optimizing complex stochastic systems. A heteroscedastic metamodel provides an accurate approximation of the input-output relationship implied by a stochastic simulation experiment whose output is subject to input-dependent noise variance. Several challenges remain unsolved in this field. First, in-depth investigations into the consistency of heteroscedastic metamodeling techniques, particularly from the sequential prediction perspective, are lacking. Second, sequential heteroscedastic metamodel-based level-set estimation (LSE) methods are scarce. Third, the increasingly high computational cost required by heteroscedastic Gaussian process-based LSE methods in the sequential sampling setting is a concern. Additionally, when constructing a valid uniform bound for a heteroscedastic metamodel, the impact of noise variance estimation is not adequately addressed. This dissertation aims to tackle these challenges and provide promising solutions. First, we investigate the information consistency of a widely used heteroscedastic metamodeling technique, stochastic kriging (SK). Second, we propose SK-based LSE methods leveraging novel uniform bounds for input-point classification. Moreover, we incorporate the Nystrom approximation and a principled budget allocation scheme to improve the computational efficiency of SK-based LSE methods. Lastly, we investigate empirical uniform bounds that take into account the impact of noise variance estimation, ensuring an adequate coverage capability. / Doctor of Philosophy / In real-world engineering problems, understanding and optimizing complex systems can be challenging and prohibitively expensive. Computer simulation is a valuable tool for analyzing and predicting system behaviors, allowing engineers to explore different scenarios without relying on costly physical prototypes. However, the increasing complexity of simulation models leads to a higher computational burden. Metamodeling techniques have emerged to address this issue by accurately approximating the system performance response surface based on limited simulation experiment data to enable real-time decision-making. Heteroscedastic metamodeling goes further by considering varying noise levels inherent in simulation outputs, resulting in more robust and accurate predictions. Among various techniques, stochastic kriging (SK) stands out by striking a good balance between computational efficiency and statistical accuracy. Despite extensive research on SK, challenges persist in its application and methodology. These include little understanding of SK's consistency properties, an absence of sequential SK-based algorithms for level-set estimation (LSE) under heteroscedasticity, and the increasingly low computational efficiency of SK-based LSE methods in implementation. Furthermore, a precise construction of uniform bounds for the SK predictor is also missing. This dissertation aims at addressing these aforementioned challenges. First, the information consistency of SK from a prediction perspective is investigated. Then, sequential SK-based procedures for LSE in stochastic simulation, incorporating novel uniform bounds for accurate input-point classification, are proposed. Furthermore, a popular approximation technique is incorporated to enhance the computational efficiency of the SK-based LSE methods. Lastly, empirical uniform bounds are investigated considering the impact of noise variance estimation.

Développer un programme capable de jouer à n’importe quel jeu de stratégie, souvent désigné par le General Game Playing (GGP) constitue un des Graal de l’intelligence artificielle. Les compétitions GGP, où chaque jeu est représenté par un ensemble de règles logiques au travers du Game Description Language (GDL), ont conduit la recherche à confronter de nombreuses approches incluant les méthodes de type Monte Carlo, la construction automatique de fonctions d’évaluation, ou la programmation logique et ASP. De par cette thèse, nous proposons une nouvelle approche dirigée par les contraintes stochastiques.Dans un premier temps, nous nous concentrons sur l’élaboration d’une traduction de GDL en réseauxde contraintes stochastiques (SCSP) dans le but de fournir une représentation dense des jeux de stratégies et permettre la modélisation de stratégies.Par la suite, nous exploitons un fragment de SCSP au travers d’un algorithme dénommé MAC-UCBcombinant l’algorithme MAC (Maintaining Arc Consistency) utilisé pour résoudre chaque niveau duSCSP tour après tour, et à l’aide de UCB (Upper Confidence Bound) afin d’estimer l’utilité de chaquestratégie obtenue par le dernier niveau de chaque séquence. L’efficacité de cette nouvelle technique sur les autres approches GGP est confirmée par WoodStock, implémentant MAC-UCB, le leader actuel du tournoi continu de GGP.Finalement, dans une dernière partie, nous proposons une approche alternative à la détection de symétries dans les jeux stochastiques, inspirée de la programmation par contraintes. Nous montrons expérimentalement que cette approche couplée à MAC-UCB, surpasse les meilleures approches du domaine et a permis à WoodStock de devenir champion GGP 2016. / The ability for a computer program to effectively play any strategic game, often referred to General Game Playing (GGP), is a key challenge in AI. The GGP competitions, where any game is represented according to a set of logical rules in the Game Description Language (GDL), have led researches to compare various approaches, including Monte Carlo methods, automatic constructions of evaluation functions, logic programming, and answer set programming through some general game players. In this thesis, we offer a new approach driven by stochastic constraints. We first focus on a translation process from GDL to stochastic constraint networks (SCSP) in order to provide compact representations of strategic games and to model strategies. In a second part, we exploit a fragment of SCSP through an algorithm called MAC-UCB by coupling the MAC (Maintaining Arc Consistency) algorithm, used to solve each stage of the SCSP in turn, together with the UCB (Upper Confidence Bound) policy for approximating the values of those strategies obtained by the last stage in the sequence. The efficiency of this technical on the others GGP approaches is confirmed by WoodStock, implementing MAC-UCB, the actual leader on the GGP Continuous Tournament. Finally, in the last part, we propose an alternative approach to symmetry detection in stochastic games, inspired from constraint programming techniques. We demonstrate experimentally that MAC-UCB, coupled with our constranit-based symmetry detection approach, significantly outperforms the best approaches and made WoodStock the GGP champion 2016.

This thesis is a collection of three essays on inflation expectations, forecasting uncertainty, and the role of uncertainty in sequential auctions, all using experimental approach. Chapter 1 studies how individuals forecast inflation in fictitious macroeconomic setup and analyzes the effect of monetary policy rules on their decisions. Results display heterogeneity in inflation forecasting rules and demonstrate the importance of adaptive learning forecasting if model switching is assumed. Chapter 2 extends the analysis from Chapter 1 by analyzing individual inflation forecasting uncertainty. Results show that confidence intervals depend on inflation variance and business cycle phase, have a strong inertia, and are often asymmetric. Finally, Chapter 3 analyzes the role of uncertainty about the number of bidders for the behavior of subjects in a sequential auction experiment. Uncertainty does not aggravate price decline, but it changes individual bidding strategies and auction efficiency. / Esta tesis consta de tres ensayos sobre las expectativas de inflación, la incertidumbre de la predicción, y la importancia de la incertidumbre en subastas secuenciales. Todos ellos utilizan un método experimental. El capítulo 1 estudia cómo los individuos predicen la inflación en la economía ficticia y analiza el efecto de las reglas de política monetaria en sus decisiones. Los resultados revelan la heterogeneidad en las reglas de predicción de la inflación y demuestran la importancia del mecanismo de aprendizaje adaptivo si el cambio entre los modelos se supone. Capítulo 2 continúa el análisis del capítulo 1, analiza la incertidumbre individual de las expectativas de inflación. Los resultados muestran que los intervalos de confianza dependen de varianza de la inflación y la fase del ciclo económico, tienen una fuerte inercia, y son frecuentemente asimétricos. Por último, el capítulo 3 analiza la influencia de la incertidumbre sobre el número de oferentes en el comportamiento de los individuos en un experimento de la subasta secuencial. La incertidumbre no agrava la caída de los precios, pero cambia las estrategias de los oferentes y la eficiencia de la subasta.