  We consider the problem of multi-objective optimization (MOO) of expensive
black-box functions with the goal of discovering high-quality and diverse
Pareto fronts where we are allowed to evaluate a batch of inputs. This problem
arises in many real-world applications including penicillin production where
diversity of solutions is critical. We solve this problem in the framework of
Bayesian optimization (BO) and propose a novel approach referred to as Pareto
front-Diverse Batch Multi-Objective BO (PDBO). PDBO tackles two important
challenges: 1) How to automatically select the best acquisition function in
each BO iteration, and 2) How to select a diverse batch of inputs by
considering multiple objectives. We propose principled solutions to address
these two challenges. First, PDBO employs a multi-armed bandit approach to
select one acquisition function from a given library. We solve a cheap MOO
problem by assigning the selected acquisition function for each expensive
objective function to obtain a candidate set of inputs for evaluation. Second,
it utilizes Determinantal Point Processes (DPPs) to choose a
Pareto-front-diverse batch of inputs for evaluation from the candidate set
obtained from the first step. The key parameters for the methods behind these
two steps are updated after each round of function evaluations. Experiments on
multiple MOO benchmarks demonstrate that PDBO outperforms prior methods in
terms of both the quality and diversity of Pareto solutions.
