Bayesian Optimization of Function Networks: Supplementary Material

In this section, we provide a formal statement and proof of Proposition 1. We begin by proving the following auxiliary result. We are now in position to show Proposition 1, which can be seen as a simple generalization of Theorem 1 in Balandat et al. (2020). R, k = 1,..., K, are Lipschitz continuous. R R, k = 1,..., K, given by f The desired result is now a direct consequence of Proposition 2 in the supplement of Balandat et al. (2020), which is in turn a consequence of Theorem 2.3 in Homem-de Mello (2008).