A novel approach to the gain estimation problem,using a multi-armed bandit formulation, is studied. The gain estimation problem deals with the problem of estimating the largest L2-gain that signal of bounded norm experiences when passing through a linear and time-invariant system. Under certain conditions, this new approach is guaranteed to surpass traditional System Identification methods in terms of accuracy.The bandit algorithms Upper Confidence Bound, Thompson Sampling and Weighted Thompson Sampling are implemented with the aim of designing the optimal input for maximizing the gain of an unknown system. The regret performance of each algorithm is studied using simulations on a test system. Upper Confidence Bound, with exploration parameter set to zero, performed the best among all tested values for this parameter. Weighted Thompson Sampling performed better than Thompson Sampling.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24939号 / 情博第850号 / 新制||情||142(附属図書館) / 京都大学大学院情報学研究科システム科学専攻 / (主査)准教授 本多 淳也, 教授 田中 利幸, 教授 鹿島 久嗣 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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Games have been a field of interest for researchin artificial intelligence for decades. As of now, it is over 5years ago an AI for the strategy game Go, AlphaGo, beat worldchampion Lee Sedol 4-1, which was considered to be an enormousmilestone for AI. Our goal is to make an AI that can play theclassic strategy board game Stratego at a competent level. Thisis achieved by making the AI learn by repeatedly playing againstitself to figure out what strategy to use in various situations byusing CFR - counterfactual regret minimization. According toour experiments, we were able to accomplish our goal in makinga Stratego AI that could play at a sophisticated level for a smallerversion of the game. We concluded that it was able to play betterthan an amateur human player. / Spel har varit ett intresseområde inomutvecklingen av artificiell intelligens i årtionden. Det är redanfem år sedan AlphaGo slog världsmästaren Lee Sedol i Go 2016,vilket betraktas vara ett stort steg för utvecklingen av AI. Vårtmål är att skapa en AI som kan spela strategispelet Stratego på en kompetent nivå. Detta kommer att implementeras genom att AI:n spelar mot sig själv en stor mängd gånger och uppdaterarsin strategi baserat på konceptet CFR counterfactual regretminimization. Enligt våra experiment lyckades vi med vårt mål i att skapa en kompetent Stratego AI för en mindre version avStratego. Vår uppfattning är att den spelar bättre än en människapå amatörnivå. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm

Many problems involving decision making withimperfect information can be modeled as extensive games. Onefamily of state-of-the-art algorithms for computing optimal playin such games is Counterfactual Regret Minimization (CFR).The purpose of this paper is to explore the viability of CFRalgorithms on the board game Stratego. We compare differentalgorithms within the family and evaluate the heuristic method“imperfect recall” for game abstraction. Our experiments showthat the Monte-Carlo variant External CFR and use of gametree pruning greatly reduce training time. Further, we show thatimperfect recall can reduce the memory requirements with only aminor drop in player performance. These results show that CFRis suitable for strategic decision making. However, solutions tothe long computation time in high complexity games need to beexplored. / Många beslutsproblem med dold informationkan modelleras som spel på omfattande form. En familj avledande algoritmer för att beräkna optimal strategi i sådana spelär Counterfactual Regret Minimization (CFR). Syftet med dennarapport är att undersöka effektiviteten för CFR-algoritmer ibrädspelet Stratego. Vi jämför olika algoritmer inom familjen ochutvärderar den heuristiska metoden “imperfekt minne” för spelabstraktion.Våra experiment visar att Monte-Carlo-variantenExternal CFR och användning av trimning av spelträd kraftigtminskar träningstiden. Vidare visar vi att imperfekt minne kanminska algoritmens lagringskrav med bara en mindre förlust ispelstyrka. Dessa resultat visar att CFR är lämplig för strategisktbeslutsfattande. Lösningar på den långa beräkningstiden i spelmed hög komplexitet måste dock undersökas. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm

Blood products are essential components of any healthcare system, and their safety, in terms of being free of transfusion-transmittable infections, is crucial. While the Food and Drug Administration (FDA) in the United States requires all blood donations to be tested for a set of infections, it does not dictate which particular tests should be used by blood collection centers. Multiple FDA-licensed blood screening tests are available for each infection, but all screening tests are imperfectly reliable and have different costs. In addition, infection prevalence rates and several donor characteristics are uncertain, while surveillance methods are highly resource- and time-intensive. Therefore, only limited information is available to budget-constrained blood collection centers that need to devise a post-donation blood screening scheme so as to minimize the risk of an infectious donation being released into the blood supply. Our focus is on "robust" screening schemes under limited information. Toward this goal, we consider various objectives, and characterize structural properties of the optimal solutions under each objective. This allows us to gain insight and to develop efficient algorithms. Our research shows that using the proposed optimization-based approaches provides robust solutions with significantly lower expected infection risk compared to other testing schemes that satisfy the FDA requirements. Our findings have important public policy implications. / Ph. D.

Les terres agricoles ont été durablement contaminées à la fois par les pesticides mis à la disposition des agriculteurs pour lutter contre les charançons et autres insectes nuisibles, et par les engrais azotées pour augmenter la productivité chez les plantes.Des recherches récentes concernent des cultures alternatives écologiques utilisant les plantes de service qui fournissent les nutriments aux plantes principales. Ce travail de thèse s'inscrit dans cette perspective, d'un point de vue modélisation.L'accent est mis sur la résolution de problèmes de contrôle du phénomène d'absorption de nutriments, par les racines dans la rhizosphère (partie proche des racines), en considérant les deux cas de sols : sol sain et sol pollué.Ces phénomènes d'absorption sont modélisés par des systèmes d'advection-diffusion de type Nye-Tinker-Barber (NTB). La concentration de nutriments absorbée, solution du problème, est une fonction du temps et de l'espace.On étudie l'existence de solution du système NTB dans les deux cas où la fonction d'absorption de nutriments à la frontière (surface de la racine) appelée fonction de Michealis-Menten, est linéaire et/ou non linéaire, à l’aide des outils d’analyse fonctionnelle. On étudie ensuite les problèmes de contrôle optimal associés au système NTB, en considérant les deux cas linéaire et non linéaire, en application pour les deux cas d’absorption de nutriments en sol non pollué puis en sol pollué. Pour le premier cas, on utilise les techniques classiques de recherche d'un contrôle pour les systèmes distribués, tandis que, pour le second cas, on fait appel aux notions de contrôle sans regret et contrôle à moindres regrets de J.-L. Lions. Les contrôles obtenus pour les différents problèmes sont caractérisés chacun par un système d'optimalité (SO) cas sans pollution, et système d’optimalité singulier (SOS) dans le cas avec pollution.= / Agriculture soils were highly contaminated for a long time by pesticides which were widely used by producers to fight against weevils. Soils where also contaminated by the use of fertilizers to increase the plant development. An ecological alternative using service plants is encouraged following recent research. The aim of this work is to give a mathematical and a modelling point of view as we study the mecha- nisms of nutrient transfer to plants using the mathematical analysis and optimal control theories. The two cases of polluted and non-polluted soils are considered. The nutrient transfer and uptake processes are modeled by an advection-diffusion system derived from the Nye-Tinker-Barber (NTB) model. The absorbed nutrient concentration represented by the Michaelis-Mention function at the root surface of the principal plant, depends on time and space. We study the existence of a solution for the linear and nonlinear NTB systems, then we characterize the opti- mal control which corresponds to the added nutrients from the service plant. For the pollution case, we use the concept of low-regret and no-regret control of J.-L. Lions.

Diese Dissertation behandelt sowohl die Theorie, als auch beobachtetes Verhalten in Stoppproblemen. In einem Stoppproblem, beobachtet ein Agent die Entwicklung eines stationären, stochastischen Prozesses über die Zeit. Zu jedem Zeitpunkt genießt der Agent das Recht den Prozess zu stoppen, um eine Auszahlung einzustreichen die Funktion des gegenwärtigen und der vergangenen Realisationen des Prozesses sind. Das Ziel des Agenten ist es den Stoppzeitpunkt so zu wählen, dass die erwartete Auszahlung oder der erwartete Verlust durch Stoppen maximiert bzw. minimiert wird. Stoppprobleme dieser Art konstituieren können als die einfachsten, jedoch wirklich dynamischen Entscheidungsprobleme in der ökonomischen Theorie angesehen werden Das erste Kapitel legt neue theoretische Resultate hinsichtlich der optimalen Stoppstrategien unter Erwartungsnutzentheorie, sog. gain-loss utilities und Bedauerungspräferenzen vor. Das zweite Kapitel behandelt sodann die Ergebnisse eines Laborexperiments in dem die theoretischen Vorhersagen getestet werden. Kapitel drei beschäftigt sich mit der Situation in der die Agenten nicht vollständig über Wahrscheinlichkeiten für künftige Ereignisse informiert sind, d.h. es herrscht Ambiguität. / This dissertation is concerned with theory and behavior in stopping problems. In a stopping problem an agent or individual observes the realization of some exogenous and stationary stochastic process over time. At every point in time, she has the right or the once-only option to stop the process in order to earn a function of the past and current values of the process. The agent''s objective then is to choose the point in time to exercise the option in order to maximize an expected reward or to minimize an expected loss. Such problems constitute the most rudimentary, yet truly dynamic class of choice problems that is studied in economics. The first chapter provides new theoretical results about optimal stopping both under expected utility, as well as gain-loss utility and regret preferences. The second chapter presents a laboratory experiment that tests several of the theoretical predictions about behavior made in the first chapter. The third chapter is concerned with stopping behavior in a setting, where the probability law that drives the observed process is not perfectly known to the decision maker, i.e. there is ambiguity.