<p dir="ltr">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.</p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/24687939 |
| Date | 01 December 2023 |
| Creators | Wenjie Li (17506956) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/_b_MODERN_BANDIT_OPTIMIZATION_WITH_STATISTICAL_GUARANTEES_b_/24687939 |
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