  We propose MUMBO, the first high-performing yet computationally efficient
acquisition function for multi-task Bayesian optimization. Here, the challenge
is to perform efficient optimization by evaluating low-cost functions somehow
related to our true target function. This is a broad class of problems
including the popular task of multi-fidelity optimization. However, while
information-theoretic acquisition functions are known to provide
state-of-the-art Bayesian optimization, existing implementations for multi-task
scenarios have prohibitive computational requirements. Previous acquisition
functions have therefore been suitable only for problems with both
low-dimensional parameter spaces and function query costs sufficiently large to
overshadow very significant optimization overheads. In this work, we derive a
novel multi-task version of entropy search, delivering robust performance with
low computational overheads across classic optimization challenges and
multi-task hyper-parameter tuning. MUMBO is scalable and efficient, allowing
multi-task Bayesian optimization to be deployed in problems with rich parameter
and fidelity spaces.
