Suggesting the best parameters for a model is often a task of optimization. If no analytical form of the function of interest is available, it is expensive to evaluate the function and the obtained observations might be noisy, one can try to perform Bayesian Optimization to optimise such function. It builds a statistical model of the function based on available observations. The model is a Gaussian process which can be parametrised in a number of ways to encode different properties of the sampled function. Then this model is refined by collecting new samples at locations suggested by an acquisition function.

We compare different kernels and parametrisations for the Gaussian Process model for the prior process. This project will also compare different acquisition functions for selection of the next observation locations. Different acquisition functions can have a different approach to a tradeoff between exploration and exploration. The true underlying function from which the samples need to be drawn is also modelled by a Gaussian Process with kernels suggested in a thesis of Witold Merkel. The performance of optimization is then compared between different kernels