# Multifidelity Bayesian Optimization for Binomial Output

## TL;DR

This paper introduces a multifidelity Bayesian optimization approach tailored for binomial output functions, leveraging a specialized Gaussian process model and an adaptive sampling strategy to efficiently optimize expensive binomial-based targets.

## Contribution

It develops a novel Gaussian process model for binomial outputs and proposes an adaptive sampling heuristic within a multifidelity Bayesian optimization framework.

## Key findings

- Effective optimization of binomial functions demonstrated
- Adaptive sampling improves efficiency and accuracy
- Model outperforms traditional Gaussian process approaches

## Abstract

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.