Multi-Fidelity Multi-Objective Bayesian Optimization: An Output Space
  Entropy Search Approach
  We study the novel problem of blackbox optimization of multiple objectives
via multi-fidelity function evaluations that vary in the amount of resources
consumed and their accuracy. The overall goal is to approximate the true Pareto
set of solutions by minimizing the resources consumed for function evaluations.
For example, in power system design optimization, we need to find designs that
trade-off cost, size, efficiency, and thermal tolerance using multi-fidelity
simulators for design evaluations. In this paper, we propose a novel approach
referred as Multi-Fidelity Output Space Entropy Search for Multi-objective
Optimization (MF-OSEMO) to solve this problem. The key idea is to select the
sequence of candidate input and fidelity-vector pairs that maximize the
information gained about the true Pareto front per unit resource cost. Our
experiments on several synthetic and real-world benchmark problems show that
MF-OSEMO, with both approximations, significantly improves over the
state-of-the-art single-fidelity algorithms for multi-objective optimization.
