112 research outputs found

    On the identification and mitigation of weaknesses in the Knowledge Gradient policy for multi-armed bandits

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    The Knowledge Gradient (KG) policy was originally proposed for online ranking and selection problems but has recently been adapted for use in online decision making in general and multi-armed bandit problems (MABs) in particular. We study its use in a class of exponential family MABs and identify weaknesses, including a propensity to take actions which are dominated with respect to both exploitation and exploration. We propose variants of KG which avoid such errors. These new policies include an index heuristic which deploys a KG approach to develop an approximation to the Gittins index. A numerical study shows this policy to perform well over a range of MABs including those for which index policies are not optimal. While KG does not make dominated actions when bandits are Gaussian, it fails to be index consistent and appears not to enjoy a performance advantage over competitor policies when arms are correlated to compensate for its greater computational demands

    The role of learning on industrial simulation design and analysis

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    The capability of modeling real-world system operations has turned simulation into an indispensable problemsolving methodology for business system design and analysis. Today, simulation supports decisions ranging from sourcing to operations to finance, starting at the strategic level and proceeding towards tactical and operational levels of decision-making. In such a dynamic setting, the practice of simulation goes beyond being a static problem-solving exercise and requires integration with learning. This article discusses the role of learning in simulation design and analysis motivated by the needs of industrial problems and describes how selected tools of statistical learning can be utilized for this purpose

    How Technology Impacts and Compares to Humans in Socially Consequential Arenas

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    One of the main promises of technology development is for it to be adopted by people, organizations, societies, and governments -- incorporated into their life, work stream, or processes. Often, this is socially beneficial as it automates mundane tasks, frees up more time for other more important things, or otherwise improves the lives of those who use the technology. However, these beneficial results do not apply in every scenario and may not impact everyone in a system the same way. Sometimes a technology is developed which produces both benefits and inflicts some harm. These harms may come at a higher cost to some people than others, raising the question: {\it how are benefits and harms weighed when deciding if and how a socially consequential technology gets developed?} The most natural way to answer this question, and in fact how people first approach it, is to compare the new technology to what used to exist. As such, in this work, I make comparative analyses between humans and machines in three scenarios and seek to understand how sentiment about a technology, performance of that technology, and the impacts of that technology combine to influence how one decides to answer my main research question.Comment: Doctoral thesis proposal. arXiv admin note: substantial text overlap with arXiv:2110.08396, arXiv:2108.12508, arXiv:2006.1262

    Exploration and exploitation in Bayes sequential decision problems

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    Bayes sequential decision problems are an extensive problem class with wide application. They involve taking actions in sequence in a system which has characteristics which are unknown or only partially known. These characteristics can be learnt over time as a result of our actions. Therefore we are faced with a trade-off between choosing actions that give desirable short term outcomes (exploitation) and actions that yield useful information about the system which can be used to improve longer term outcomes (exploration). Gittins indices provide an optimal method for a small but important subclass of these problems. Unfortunately the optimality of index methods does not hold generally and Gittins indices can be impractical to calculate for many problems. This has motivated the search for easy-to-calculate heuristics with general application. One such non-index method is the knowledge gradient heuristic. A thorough investigation of the method is made which identifies crucial weaknesses. Index and non-index variants are developed which avoid these weaknesses. The problem of choosing multiple website elements to present to user is an important problem relevant to many major web-based businesses. A Bayesian multi-armed bandit model is developed which captures the interactions between elements and the dual uncertainties of both user preferences and element quality. The problem has many challenging features but solution methods are proposed that are both easy to implement and which can be adapted to particular applications. Finally, easy-to-use software to calculate Gittins indices for Bernoulli and normal rewards has been developed as part of this thesis and has been made publicly available. The methodology used is presented together with a study of accuracy and speed

    Motion Planning for Autonomous Vehicles in Partially Observable Environments

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    Unsicherheiten, welche aus Sensorrauschen oder nicht beobachtbaren Manöverintentionen anderer Verkehrsteilnehmer resultieren, akkumulieren sich in der Datenverarbeitungskette eines autonomen Fahrzeugs und führen zu einer unvollständigen oder fehlinterpretierten Umfeldrepräsentation. Dadurch weisen Bewegungsplaner in vielen Fällen ein konservatives Verhalten auf. Diese Dissertation entwickelt zwei Bewegungsplaner, welche die Defizite der vorgelagerten Verarbeitungsmodule durch Ausnutzung der Reaktionsfähigkeit des Fahrzeugs kompensieren. Diese Arbeit präsentiert zuerst eine ausgiebige Analyse über die Ursachen und Klassifikation der Unsicherheiten und zeigt die Eigenschaften eines idealen Bewegungsplaners auf. Anschließend befasst sie sich mit der mathematischen Modellierung der Fahrziele sowie den Randbedingungen, welche die Sicherheit gewährleisten. Das resultierende Planungsproblem wird mit zwei unterschiedlichen Methoden in Echtzeit gelöst: Zuerst mit nichtlinearer Optimierung und danach, indem es als teilweise beobachtbarer Markov-Entscheidungsprozess (POMDP) formuliert und die Lösung mit Stichproben angenähert wird. Der auf nichtlinearer Optimierung basierende Planer betrachtet mehrere Manöveroptionen mit individuellen Auftrittswahrscheinlichkeiten und berechnet daraus ein Bewegungsprofil. Er garantiert Sicherheit, indem er die Realisierbarkeit einer zufallsbeschränkten Rückfalloption gewährleistet. Der Beitrag zum POMDP-Framework konzentriert sich auf die Verbesserung der Stichprobeneffizienz in der Monte-Carlo-Planung. Erstens werden Informationsbelohnungen definiert, welche die Stichproben zu Aktionen führen, die eine höhere Belohnung ergeben. Dabei wird die Auswahl der Stichproben für das reward-shaped Problem durch die Verwendung einer allgemeinen Heuristik verbessert. Zweitens wird die Kontinuität in der Reward-Struktur für die Aktionsauswahl ausgenutzt und dadurch signifikante Leistungsverbesserungen erzielt. Evaluierungen zeigen, dass mit diesen Planern große Erfolge in Fahrversuchen und Simulationsstudien mit komplexen Interaktionsmodellen erreicht werden

    Experimenting with sequential allocation procedures

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    In experiments that consider the use of subjects, a crucial part is deciding which treatment to allocate to which subject – in other words, constructing the treatment allocation procedure. In a classical experiment, this treatment allocation procedure often simply constitutes randomly assigning subjects to a number of different treatments. Subsequently, when all outcomes have been observed, the resulting data is used to conduct an analysis that is specified a priori. Practically, however, the subjects often arrive at an experiment one-by-one. This allows the data generating process to be viewed differently: instead of considering the subjects in a batch, intermediate data from previous interactions with other subjects can be used to influence the decisions of the treatment allocation in future interactions. A heavily researched formalization that helps developing strategies for sequentially allocating subjects is the multi-armed bandit problem. In this thesis, several methods are developed to expedite the use of sequential allocation procedures by (social) scientists in field experiments. This is done by building upon the extensive literature of the multi-armed bandit problem. The thesis also introduces and shows many (empirical) examples of the usefulness and applicability of sequential allocation procedures in practice

    Poisson process bandits:Sequential models and algorithms for maximising the detection of point data

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    In numerous settings in areas as diverse as security, ecology, astronomy, and logistics, it is desirable to optimally deploy a limited resource to observe events, which may be modelled as point data arising according to a Non-homogeneous Poisson process. Increasingly, thanks to developments in mobile and adaptive technologies, it is possible to update a deployment of such resource and gather feedback on the quality of multiple actions. Such a capability presents the opportunity to learn, and with it a classic problem in operations research and machine learning - the explorationexploitation dilemma. To perform optimally, how should investigative choices which explore the value of poorly understood actions and optimising choices which choose actions known to be of a high value be balanced? Effective techniques exist to resolve this dilemma in simpler settings, but the Poisson process data brings new challenges. In this thesis, effective solution methods for the problem of sequentially deploying resource are developed, via a combination of efficient inference schemes, bespoke optimisation approaches, and advanced sequential decision-making strategies. Furthermore, extensive theoretical work provides strong guarantees on the performance of the proposed solution methods and an understanding of the challenges of this problem and more complex extensions. In particular, Upper Confidence Bound and Thompson Sampling (TS) approaches are derived for combinatorial and continuum-armed bandit versions of the problem, with accompanying analysis displaying that the regret of the approaches is of optimal order. A broader understanding of the performance of TS based on non-parametric models for smooth reward functions is developed, and new posterior contraction results for the Gaussian Cox Process, a popular Bayesian non-parametric model of point data, are derived. These results point to effective strategies for more challenging variants of the event detection problem, and more generally advance the understanding of bandit decision-making with complex data structures

    The Finite-Horizon Two-Armed Bandit Problem with Binary Responses:A Multidisciplinary Survey of the History, State of the Art, and Myths

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    In this paper we consider the two-armed bandit problem, which often naturally appears per se or as a subproblem in some multi-armed generalizations, and serves as a starting point for introducing additional problem features. The consideration of binary responses is motivated by its widespread applicability and by being one of the most studied settings. We focus on the undiscounted finite-horizon objective, which is the most relevant in many applications. We make an attempt to unify the terminology as this is different across disciplines that have considered this problem, and present a unified model cast in the Markov decision process framework, with subject responses modelled using the Bernoulli distribution, and the corresponding Beta distribution for Bayesian updating. We give an extensive account of the history and state of the art of approaches from several disciplines, including design of experiments, Bayesian decision theory, naive designs, reinforcement learning, biostatistics, and combination designs. We evaluate these designs, together with a few newly proposed, accurately computationally (using a newly written package in Julia programming language by the author) in order to compare their performance. We show that conclusions are different for moderate horizons (typical in practice) than for small horizons (typical in academic literature reporting computational results). We further list and clarify a number of myths about this problem, e.g., we show that, computationally, much larger problems can be designed to Bayes-optimality than what is commonly believed

    Approximate Dynamic Programming: Health Care Applications

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    This dissertation considers different approximate solutions to Markov decision problems formulated within the dynamic programming framework in two health care applications. Dynamic formulations are appropriate for problems which require optimization over time and a variety of settings for different scenarios and policies. This is similar to the situation in a lot of health care applications for which because of the curses of dimensionality, exact solutions do not always exist. Thus, approximate analysis to find near optimal solutions are motivated. To check the quality of approximation, additional evidence such as boundaries, consistency analysis, or asymptotic behavior evaluation are required. Emergency vehicle management and dose-finding clinical trials are the two heath care applications considered here in order to investigate dynamic formulations, approximate solutions, and solution quality assessments. The dynamic programming formulation for real-time ambulance dispatching and relocation policies, response-adaptive dose-finding clinical trial, and optimal stopping of adaptive clinical trials is presented. Approximate solutions are derived by multiple methods such as basis function regression, one-step look-ahead policy, simulation-based gridding algorithm, and diffusion approximation. Finally, some boundaries to assess the optimality gap and a proof of consistency for approximate solutions are presented to ensure the quality of approximation
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