Treffer: Targeted Variance Reduction: Effective Bayesian Optimization of Black-Box Simulators with Noise Parameters.

The optimization of a black-box simulator over control parameters x arises in a myriad of scientific applications. In such applications, the simulator often takes the form f (x , θ) , where θ are parameters that are uncertain in practice. Stochastic optimization aims to optimize the objective E [ f (x , Θ) ] , where Θ ∼ P is a random variable that models uncertainty on θ . For this, existing black-box methods typically employ a two-stage approach for selecting the next point (x , θ) , where x and θ are optimized separately via different acquisition functions. As such, these approaches do not employ a joint acquisition over (x , θ) , and thus may fail to fully exploit control-to-noise interactions for effective stochastic optimization. To address this, we propose a new Bayesian optimization method called Targeted Variance Reduction (TVR). The TVR leverages a novel joint acquisition function over (x , θ) , which targets variance reduction on the objective within the desired region of improvement. Under a Gaussian process surrogate with a squared exponential covariance function on f, the TVR acquisition can be evaluated in closed form, and reveals an insightful exploration-exploitation-precision tradeoff for stochastic black-box optimization. The TVR can further accommodate a broad class of non-Gaussian distributions on P via a careful integration of normalizing flows. We demonstrate the improved performance of TVR over the state-of-the-art in a suite of numerical experiments and an application to the robust design of automobile brake discs under operational uncertainty. [ABSTRACT FROM AUTHOR]

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