  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.
