Designing over uncertain outcomes with stochastic sampling Bayesian optimization

TL;DR

This paper introduces stochastic sampling Bayesian optimization (SSBO), a new framework for optimizing uncertain outcomes in scientific and engineering problems, incorporating stochasticity into the Bayesian optimization process.

Contribution

The paper proposes SSBO, adapting Bayesian optimization to handle stochastic outcomes and developing techniques to limit myopic decisions in batch settings, with theoretical and applied validations.

Findings

SSBO bounds on expected regret resemble traditional Bayesian optimization with added stochastic penalties.

SSBO effectively optimizes standard benchmark problems with uncertain outcomes.

SSBO successfully applied to a bioengineering-inspired optimization task.

Abstract

Optimization is becoming increasingly common in scientific and engineering domains. Oftentimes, these problems involve various levels of stochasticity or uncertainty in generating proposed solutions. Therefore, optimization in these scenarios must consider this stochasticity to properly guide the design of future experiments. Here, we adapt Bayesian optimization to handle uncertain outcomes, proposing a new framework called stochastic sampling Bayesian optimization (SSBO). We show that the bounds on expected regret for an upper confidence bound search in SSBO resemble those of earlier Bayesian optimization approaches, with added penalties due to the stochastic generation of inputs. Additionally, we adapt existing batch optimization techniques to properly limit the myopic decision making that can arise when selecting multiple instances before feedback. Finally, we show that SSBO techniques properly optimize a set of standard optimization problems as well as an applied problem inspired by bioengineering.