A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations

Abstract

Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the evaluation of the functions in question are expensive. Traditional methods for multi-objective optimization, both Bayesian and otherwise, are aimed at recovering the Pareto front of these objectives. However, in certain cases a practitioner might desire to identify Pareto optimal points only in a subset of the Pareto front due to external considerations. In this work, we propose a strategy based on random scalarizations of the objectives that addresses this problem. Our approach is able to flexibly sample from desired regions of the Pareto front and, computationally, is considerably cheaper than most approaches for MOO. We also study a notion of regret in the multi-objective setting and show that our strategy achieves sublinear regret. We experiment with both synthetic and real-life problems, and demonstrate superior performance of our proposed algorithm in terms of the flexibility and regret.

arXiv commentAccepted to UAI 2019

References in corpus (9)

• Practical Bayesian Optimization of Machine Learning Algorithms
• Practical and Optimal LSH for Angular Distance
• Predictive Entropy Search for Multi-objective Bayesian Optimization
• A Bayesian model selection analysis of WMAP3
• Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints
• Tuning Hyperparameters without Grad Students: Scalable and Robust Bayesian Optimisation with Dragonfly
• Bayesian Optimization for Synthetic Gene Design
• Learning Probability Measures with respect to Optimal Transport Metrics
• Query Efficient Posterior Estimation in Scientific Experiments via Bayesian Active Learning

Cited by in corpus (12)

• Autonomous discovery of battery electrolytes with robotic experimentation and machine-learning
• SpArSe: Sparse Architecture Search for CNNs on Resource-Constrained Microcontrollers
• Tuning Hyperparameters without Grad Students: Scalable and Robust Bayesian Optimisation with Dragonfly
• Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement
• Multi-objective Bayesian Optimization using Pareto-frontier Entropy
• Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces
• Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization
• Pareto Front-Diverse Batch Multi-Objective Bayesian Optimization
• Scalable Thompson Sampling using Sparse Gaussian Process Models
• Balancing Competing Objectives with Noisy Data: Score-Based Classifiers for Welfare-Aware Machine Learning
• Multi-armed Bandits with Cost Subsidy
• Advancing the Pareto front for thin-film materials using a self-driving laboratory