Efficient Bayesian Optimization for Target Vector Estimation
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Proceedings of Machine Learning Research, PMLR 89:26612670, 2019.
Abstract
We consider the problem of estimating a target vector by querying an unknown multioutput function which is stochastic and expensive to evaluate. Through sequential experimental design the aim is to minimize the squared Euclidean distance between the output of the function and the target vector. Applying standard singleobjective Bayesian optimization to this problem is both wasteful, since individual output components are never observed, and imprecise since the predictive distribution for new inputs will be symmetric and have negative support. We address this issue by proposing a Gaussian process model that considers the individual function outputs and derive a distribution over the resulting 2norm. Furthermore we derive computationally efficient acquisition functions and evaluate the resulting optimization framework on several synthetic problems and a realworld problem. The results demonstrate a significant improvement over Bayesian optimization based on both standard and warped Gaussian processes.
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