Bayesian Optimization with Empirical Constraints Bayesian Optimization (BO) methods are often used to optimize an unknown function f(.) that is costly to evaluate. They typically work in an
iterative manner. In each iteration, given a set of observation points, BO algorithms select k>=1 points to be evaluated. The results of those experiments are then added to the set of
observations and the procedure is repeated until a stopping criteria is met. The goal is to optimize the function f(.) with minimum number of experiment evaluations. While this problem has been
extensively studied, most existing approaches ignored some real constraints frequently encountered in practical applications. In this thesis, we extend the BO framework in a number of
important directions to address some of these constraints.

First, we introduce a constrained BO framework where instead of selecting a precise point at each iteration, we request a constrained
experiment which is characterized by a hyper-rectangle in the input space. We introduce efficient sequential and non-sequential algorithms which select a set of constrained experiments that best
optimize f(.) within a given budget. Second, we introduce one of the first attempts in batch BO where instead of selecting one experiment at each iteration, a set of k>1 experiments is selected.
This can significantly speedup the overall running time of BO. Third, we introduce scheduling algorithms for the BO framework when: 1) it is possible to run concurrent experiments; 2) the durations
of experiments running time are stochastic, but with a known distribution; and 3) there is a limited number of experiments to run in a fixed amount of time. We propose both online and offline
scheduling algorithms which effectively handle these constraints. Finally, we introduce a hybrid BO approach which switches between sequential and batch mode. The proposed hybrid approach provides
us with a substantial speedup against sequential policies without significant performance loss.

Major Advisor: Xiaoli Fern Committee: Alan
Fern Committee: Prasad Tadepalli Committee:
Weng-Keen Wong GCR: Shoichi Kimura