An Adaptive Batch Bayesian Optimization Approach for Expensive Multi-Objective Optimization problems

Abstract

This paper presents Adaptive Batch-ParEGO, an adaptive batch Bayesian optimization method for expensive multi-objective problems. This method extends the classical multi-objective Bayesian optimization method, sequential ParEGO, to the batch mode. Specifically, the proposed method exploits a newly proposed bi-objective acquisition func- tion to recommend and evaluate multiple solutions. The bi-objective acquisition function takes exploitation and exploration as two optimization objectives, which are traded off by a multi-objective evolutionary algorithm. Since there’s usually a certain number of lim- ited hardware resources available in reality, we further propose an adaptive solution selec- tion criterion to fix the number of candidate solutions in each iteration. This strategy dynamically balances exploitation and exploration by tuning the hyper-parameter in the exploitation-exploration fitness function. In addition, the expected improvement is exploited to select another candidate solution to ensure convergence and make the algo- rithm more robust. We verify the effectiveness of Adaptive Batch-ParEGO on three multi-objective benchmarks and a hyperparameter tuning task of neural networks com- pared with the state-of-the-art multi-objective approaches. Our analysis demonstrates that the bi-objective acquisition function with the adaptive recommendation strategy can bal- ance exploitation and exploration well in batch mode for expensive multi-objective prob- lems. All our source codes will be published at https://github.com/thuiar/Adaptive-Batch-ParEGO.