  We consider the problem of robust optimization within the well-established
Bayesian optimization (BO) framework. While BO is intrinsically robust to noisy
evaluations of the objective function, standard approaches do not consider the
case of uncertainty about the input parameters. In this paper, we propose
Noisy-Input Entropy Search (NES), a novel information-theoretic acquisition
function that is designed to find robust optima for problems with both input
and measurement noise. NES is based on the key insight that the robust
objective in many cases can be modeled as a Gaussian process, however, it
cannot be observed directly. We evaluate NES on several benchmark problems from
the optimization literature and from engineering. The results show that NES
reliably finds robust optima, outperforming existing methods from the
literature on all benchmarks.
