  The key idea of Bayesian optimization is replacing an expensive target
function with a cheap surrogate model. By selection of an acquisition function
for Bayesian optimization, we trade off between exploration and exploitation.
The acquisition function typically depends on the mean and the variance of the
surrogate model at a given point.
  The most common Gaussian process-based surrogate model assumes that the
target with fixed parameters is a realization of a Gaussian process. However,
often the target function doesn't satisfy this approximation. Here we consider
target functions that come from the binomial distribution with the parameter
that depends on inputs. Typically we can vary how many Bernoulli samples we
obtain during each evaluation.
  We propose a general Gaussian process model that takes into account Bernoulli
outputs. To make things work we consider a simple acquisition function based on
Expected Improvement and a heuristic strategy to choose the number of samples
at each point thus taking into account precision of the obtained output.
