Bayesian Optimization for Intrinsically Noisy Response Surfaces - Van Beek, Anton; ICASP14 (My University, 2023)
While Bayesian optimization (BO) is a well-established method for efficient optimization of deterministic response surfaces that are time intensive to evaluate, its application for the optimization of stochastic response surfaces is still an elusive objective. Stochastic response surfaces are functions that manifest intrinsic uncertainty so that when they are evaluated for the same inputs a variation in the output can be observed. These types of response surfaces are encountered when doing physical experiments and some forms of simulation experiments (e.g., molecular dynamics, and agent-based models). One primary advantage of BO is that it provides a systematic approach to sequentially identify the next most appropriate input conditions to evaluate, thus saving experimental resources. Moreover, the sampling decisions are made by maximizing an acquisition function that balances the mean of a posterior predictive distribution (i.e., a Bayesian-based response surface approximation conditioned on the available training data set) with the interpolation uncertainty (i.e., exploitation versus exploration). The challenge when using BO to optimize the mean of a stochastic function lies in the need to obtain a posterior predictive distribution that can quantify the intrinsic modeling uncertainty from the interpolation uncertainty. However, establishing such a posterior predictive distribution is a data-intensive task, and thus simplifying assumptions often need to be made when implementing the BO framework to optimize stochastic response surfaces. In this talk, we will present a systematic empirical investigation into the effect that decisions in the construction of the posterior predictive distribution (e.g., choice of covariance function, acquisition function, the use of replicates, and initial batch size) and the properties of the response surface (e.g., noise magnitude, problem dimension, and noise form) have on the efficiency of the BO process. Through this effort we can make the following two knowledge claims about BO in the context of stochastic response surfaces: 1. The obtained insight enables engineers and scientists to use prior knowledge of the properties of the response surface to inform the construction of the posterior predictive distribution in BO. 2. It highlights under what conditions it is appropriate to use the BO framework for the optimization of stochastic functions. Finally, we will use the presented study to explore how the BO framework can be improved to be more appropriate for the optimization of stochastic functions. This effort holds the potential to revolutionize how engineers and scientists design their experimental studies and pivot around quantifying intrinsic modeling uncertainty and interpolation uncertainty.
14th International Conference on Applications of Statistics and Probability in Civil Engineering(ICASP14)
PUBLISHED