  Many real-world applications involve black-box optimization of multiple
objectives using continuous function approximations that trade-off accuracy and
resource cost of evaluation. For example, in rocket launching research, we need
to find designs that trade-off return-time and angular distance using
continuous-fidelity simulators (e.g., varying tolerance parameter to trade-off
simulation time and accuracy) for design evaluations. The goal is to
approximate the optimal Pareto set by minimizing the cost for evaluations. In
this paper, we propose a novel approach referred to as information-Theoretic
Multi-Objective Bayesian Optimization with Continuous Approximations (iMOCA)}
to solve this problem. The key idea is to select the sequence of input and
function approximations for multiple objectives which maximize the information
gain per unit cost for the optimal Pareto front. Our experiments on diverse
synthetic and real-world benchmarks show that iMOCA significantly improves over
existing single-fidelity methods.
