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Guarantees for a few structured statistical problems


In recent years, we have seen a tremendous interest in applying statistics and machine learning methods in various areas of science: health, education, drug design, public policy design to name a few. This immense popularity of statistical methods comes with challenging new questions which lie in the boundary of theoretical and methodological aspects of statistics, machine learning and optimization. The aim of this dissertation is to address some of the these challenges that arise in modern reinforcement learning, and in modern data science practice and provide new insights that are helpful to practitioners. The dissertation is divided into four parts. In Part I we discuss principled ways of designing fast algorithms for various reinforcement learning problems. The Part II of the dissertation is devoted to problems that arise due to model misspecification. In Part III we discuss how can we perform inference when the data set is collected in a sequential manner; i.e. the helpful iid structure is not present in the data. Finally, Part IV focuses on deriving fast algorithms for structured non-convex problems.

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