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Learning theory is a dynamic and rapidly evolving field that aims to provide mathematical foundations for designing and understanding the behavior of algorithms and procedures that can learn from data automatically. At the heart of this field lies the interplay between algorithm design and statistical complexity analysis, with sharp statistical complexity characterizations often requiring localization analysis. This dissertation aims to advance the fields of machine learning and decision making by contributing to two key directions: principled algorithm design and localized statistical complexity. Our research develops novel algorithmic techniques and analytical frameworks to build more effective and robust learning systems. Specifically, we focus on studying uniform convergence and localization in statistical learning theory, developing efficient algorithms using the optimism principle for contextual bandits, and creating Bayesian design principles for bandit and reinforcement learning problems. |
