Abstract
We develop the first Bayesian Optimization algorithm, BLOSSOM, which selects between multiple alternative acquisition functions and traditional local optimization at each step. This is co bined with a novel stopping condition based on expected regret. This pairing allows us to obtain th best characteristics of both local and Bayesian op timization, making efficient use of function evalu ations while yielding superior convergence to the global minimum on a selection of optimization problems, and also halting optimization once a principled and intuitive stopping condition has been fulfilled.