Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input noise, resulting in a product that is often less performant than expected. Although BO methods have been proposed for optimizing a single objective under input noise, no existing method addresses the practical scenario where there are multiple objectives that are sensitive to input perturbations. In this work, we propose the first multi-objective BO method that is robust to input noise. We formalize our goal as optimizing the multivariate value-at-risk (MVaR), a risk measure of the uncertain objectives. Since directly optimizing MVaR is computationally infeasible in many settings, we propose a scalable, theoretically-grounded approach for optimizing MVaR using random scalarizations. Empirically, we find that our approach significantly outperforms alternative methods and efficiently identifies optimal robust designs that will satisfy specifications across multiple metrics with high probability.
翻译:贝叶斯优化(BO)是调整设计参数以优化昂贵到估价的黑箱性能度量的抽样有效方法。在许多制造过程中,设计参数受到随机输入噪音的影响,导致产品性能往往不如预期。虽然提出了BO在输入噪音下优化单一目标的方法,但没有现行方法处理对输入扰动敏感的多种目标的实际设想。在这项工作中,我们提出了第一个对输入噪音具有强力的多目标BO方法。我们正式确定了我们的目标,即优化多变量风险值(MVaR),这是不确定目标的一种风险衡量标准。由于直接优化MVAR在许多环境中是计算上不可能的,我们提出了一种可扩缩的、有理论基础的方法,用随机的斜度来优化MVAR。我们发现,我们的方法大大优于其他方法,并有效地确定了符合多个指标的规格的最佳可靠设计。