Pareto Front-Diverse Batch Multi-Objective Bayesian Optimization

Abstract

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.

Published at AAAI Conference on Artificial Intelligence, 2024

References in corpus (20)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Determinantal point processes for machine learning
• Predictive Entropy Search for Efficient Global Optimization of Black-box Functions
• Max-value Entropy Search for Efficient Bayesian Optimization
• Predictive Entropy Search for Multi-objective Bayesian Optimization
• Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization
• Portfolio Allocation for Bayesian Optimization
• Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement
• Batched Gaussian Process Bandit Optimization via Determinantal Point Processes
• A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations
• Multi-Objective Quality Diversity Optimization
• Pareto Set Learning for Expensive Multi-Objective Optimization
• Batched High-dimensional Bayesian Optimization via Structural Kernel Learning
• Multi-objective Bayesian Optimization using Pareto-frontier Entropy
• Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces
• Multi-objective Bayesian optimisation with preferences over objectives
• Joint Entropy Search for Maximally-Informed Bayesian Optimization
• Multi-Attribute Bayesian Optimization With Interactive Preference Learning
• Multi-Objective GFlowNets
• Diversified Sampling for Batched Bayesian Optimization with Determinantal Point Processes