  We develop a framework for warm-starting Bayesian optimization, that reduces
the solution time required to solve an optimization problem that is one in a
sequence of related problems. This is useful when optimizing the output of a
stochastic simulator that fails to provide derivative information, for which
Bayesian optimization methods are well-suited. Solving sequences of related
optimization problems arises when making several business decisions using one
optimization model and input data collected over different time periods or
markets. While many gradient-based methods can be warm started by initiating
optimization at the solution to the previous problem, this warm start approach
does not apply to Bayesian optimization methods, which carry a full metamodel
of the objective function from iteration to iteration. Our approach builds a
joint statistical model of the entire collection of related objective
functions, and uses a value of information calculation to recommend points to
evaluate.
