Multifidelity Bayesian Optimization for Binomial Output
This work addresses a specific limitation in Bayesian optimization for functions with non-Gaussian, binomial noise, which is incremental as it extends existing methods to handle a particular type of output distribution.
The paper tackles the problem of Bayesian optimization for target functions with binomial outputs, which do not fit the standard Gaussian process assumption, by proposing a Gaussian process model that accounts for Bernoulli outputs and a heuristic strategy for sample allocation. The result is a method that adaptively chooses the number of Bernoulli samples at each evaluation point to balance precision and efficiency.
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.