Deterministic global optimization with Gaussian processes embedded

Gaussian Processes for Global Optimization

In this paper we frame global optimization as a sequential decision problem. Imagine that we have an unknown and expensive-to-evaluate objective function y(x) that we seek to minimize. The cost associated with computing y(x) compels us to select the location of each new evaluation very carefully. Our problem’s ultimate task is to return a final point xM in the domain, and we define the loss ass...

Safe Exploration for Optimization with Gaussian Processes

We consider sequential decision problems under uncertainty, where we seek to optimize an unknown function from noisy samples. This requires balancing exploration (learning about the objective) and exploitation (localizing the maximum), a problem well-studied in the multiarmed bandit literature. In many applications, however, we require that the sampled function values exceed some prespecified “...

Global Optimization with the Gaussian Polytree EDA

This paper introduces the Gaussian polytree estimation of distribution algorithm, a new construction method, and its application to estimation of distribution algorithms in continuous variables. The variables are assumed to be Gaussian. The construction of the tree and the edges orientation algorithm are based on information theoretic concepts such as mutual information and conditional mutual i...

Global Optimization Using Embedded Graphs

One of the challenges of computer vision is that the information we seek to extract from images is not even defined for most images. Because of this, we cannot hope to find a simple process that produces the information directly from a given image. Instead, we need a search, or an optimization, in the space of parameters that we are trying to estimate. In this thesis, I introduce two new optimi...

A deterministic algorithm for global optimization