Robust Bayesian Target Value Optimization
This work solves the target value optimization problem for stochastic systems, such as in industrial processes, but it is incremental as it extends existing Bayesian optimization methods.
The paper addresses the problem of optimizing a stochastic black-box function to match a target value by considering both expectation and variance of the output, deriving acquisition functions for criteria like expected improvement. The experiments show that these functions outperform classical Bayesian optimization, even when assumptions are violated, with an industrial application in billet forging.
We consider the problem of finding an input to a stochastic black box function such that the scalar output of the black box function is as close as possible to a target value in the sense of the expected squared error. While the optimization of stochastic black boxes is classic in (robust) Bayesian optimization, the current approaches based on Gaussian processes predominantly focus either on i) maximization/minimization rather than target value optimization or ii) on the expectation, but not the variance of the output, ignoring output variations due to stochasticity in uncontrollable environmental variables. In this work, we fill this gap and derive acquisition functions for common criteria such as the expected improvement, the probability of improvement, and the lower confidence bound, assuming that aleatoric effects are Gaussian with known variance. Our experiments illustrate that this setting is compatible with certain extensions of Gaussian processes, and show that the thus derived acquisition functions can outperform classical Bayesian optimization even if the latter assumptions are violated. An industrial use case in billet forging is presented.