Towards Practical Theory: Bayesian Optimization and Optimal Exploration

Unknown author (2016-05-26)

SM thesis

This thesis discusses novel principles to improve the theoretical analyses of a class of methods, aiming to provide theoretically driven yet practically useful methods. The thesis focuses on a class of methods, called bound-based search, which includes several planning algorithms (e.g., the A* algorithm and the UCT algorithm), several optimization methods (e.g., Bayesian optimization and Lipschitz optimization), and some learning algorithms (e.g., PAC-MDP algorithms). For Bayesian optimization, this work solves an open problem and achieves an exponential convergence rate. For learning algorithms, this thesis proposes a new analysis framework, called PAC-RMDP, and improves the previous theoretical bounds. The PAC-RMDP framework also provides a unifying view of some previous near-Bayes optimal and PAC-MDP algorithms. All proposed algorithms derived on the basis of the new principles produced competitive results in our numerical experiments with standard benchmark tests.

Creative Commons Attribution 4.0 International
Except where otherwise noted, this item's license is described as Creative Commons Attribution 4.0 International