Information-Theoretic Multi-Objective Bayesian Optimization with Continuous Approximations

TL;DR

This paper introduces iMOCA, an information-theoretic multi-objective Bayesian optimization method that efficiently balances evaluation cost and accuracy using continuous approximations to find Pareto optimal solutions.

Contribution

The paper presents a novel multi-objective Bayesian optimization approach that actively selects continuous approximations to maximize information gain per cost, improving efficiency over existing methods.

Findings

iMOCA outperforms single-fidelity methods on synthetic benchmarks.

It effectively balances cost and accuracy in multi-objective optimization.

Demonstrates significant improvements in real-world applications like rocket design.

Abstract

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.