Co-Learning Bayesian Optimization
Zhendong Guo, Yew-Soon Ong, Tiantian He, Haitao Liu
TL;DR
Co-Learning Bayesian Optimization (CLBO) tackles suboptimal Bayesian optimization caused by surrogate inaccuracies near the true optimum by introducing a co-learning framework that combines model diversity with agreement on unlabeled information. It uses a full-data single-output GP (SOGP) and multiple agreement-assisted multi-output GPs (MFGP) trained on diverse subsets, with a curve-bumpiness constraint enforced across the MFGP to balance bias-variance effects. Sample search employs EI augmented by pseudo-EI (PEI) and a sample-exchange mechanism between models to preserve diversity while sharing information about promising regions. Empirical results on five numerical benchmarks and three engineering tasks show CLBO often achieving best or near-best final solutions with robust convergence, validating its potential for more efficient and reliable black-box optimization in robotics and design problems.
Abstract
Bayesian optimization (BO) is well known to be sample-efficient for solving black-box problems. However, the BO algorithms can sometimes get stuck in suboptimal solutions even with plenty of samples. Intrinsically, such suboptimal problem of BO can attribute to the poor surrogate accuracy of the trained Gaussian process (GP), particularly that in the regions where the optimal solutions locate. Hence, we propose to build multiple GP models instead of a single GP surrogate to complement each other and thus resolving the suboptimal problem of BO. Nevertheless, according to the bias-variance tradeoff equation, the individual prediction errors can increase when increasing the diversity of models, which may lead to even worse overall surrogate accuracy. On the other hand, based on the theory of Rademacher complexity, it has been proved that exploiting the agreement of models on unlabeled information can help to reduce the complexity of the hypothesis space, and therefore achieving the required surrogate accuracy with fewer samples. Such value of model agreement has been extensively demonstrated for co-training style algorithms to boost model accuracy with a small portion of samples. Inspired by the above, we propose a novel BO algorithm labeled as co-learning BO (CLBO), which exploits both model diversity and agreement on unlabeled information to improve the overall surrogate accuracy with limited samples, and therefore achieving more efficient global optimization. Through tests on five numerical toy problems and three engineering benchmarks, the effectiveness of proposed CLBO has been well demonstrated.