A Theoretical Framework for Bayesian Optimization Convergence

Abstract: Bayesian optimization is a well known class of derivative-free optimization algorithms mainly used for expensive black-box objective functions. Despite their efficiency, they suffer from a lack of rigorous convergence criterion which makes them more prone to be used as modeling tools rather than optimizing tools. This master thesis proposes, analyzes, and tests a globally convergent framework (that is to say the convergence to a stationary point regardless the initial sample) for Bayesian optimization algorithms. The framework design intends to preserve the global search characteristics for minimum while being rigorously monitored to converge.