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MODERN BANDIT OPTIMIZATION WITH STATISTICAL GUARANTEES

thesis
posted on 2023-12-01, 14:40 authored by Wenjie LiWenjie Li

Bandit and optimization represent prominent areas of machine learning research. Despite extensive prior research on these topics in various contexts, modern challenges, such as deal- ing with highly unsmooth nonlinear reward objectives and incorporating federated learning, have sparked new discussions. The X-armed bandit problem is a specialized case where bandit algorithms and blackbox optimization techniques join forces to address noisy reward functions within continuous domains to minize the regret. This thesis concentrates on the X -armed bandit problem in a modern setting. In the first chapter, we introduce an optimal statistical collaboration framework for the single-client X -armed bandit problem, expanding the range of objectives by considering more general smoothness assumptions and empha- sizing tighter statistical error measures to expedite learning. The second chapter addresses the federated X-armed bandit problem, providing a solution for collaboratively optimizing the average global objective while ensuring client privacy. In the third chapter, we confront the more intricate personalized federated X -armed bandit problem. An enhanced algorithm facilitating the simultaneous optimization of all local objectives is proposed.

History

Degree Type

  • Doctor of Philosophy

Department

  • Statistics

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Qifan Song

Advisor/Supervisor/Committee co-chair

Jean Honorio

Additional Committee Member 2

Yichen Zhang

Additional Committee Member 3

Nianqiao Ju

Additional Committee Member 4

Jun Xie

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