An adaptive batch Bayesian optimization approach for expensive multi-objective problems

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 function 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 limited hardware resources available in reality, we further propose an adaptive solution selection 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 algorithm more robust. We verify the effectiveness of Adaptive Batch-ParEGO on three multi-objective benchmarks and a hyperparameter tuning task of neural networks compared with the state-of-the-art multi-objective approaches. Our analysis demonstrates that the bi-objective acquisition function with the adaptive recommendation strategy can balance exploitation and exploration well in batch mode for expensive multi-objective problems. All our source codes will be published at https://github.com/thuiar/Adaptive-Batch-ParEGO.