New Bayesian optimization algorithm using a sequential Monte-Carlo approach
This thesis deals with the problem of global optimization of expensive-to-evaluate functions in a Bayesian framework. We say that a function is expensive-to-evaluate when its evaluation requires a significant amount of resources (e.g., very long numerical simulations).In this context, it is important to use optimization algorithms that can deal with a limited number of function evaluations. We consider here a Bayesian approach which consists in assigning a prior to the function, under the form of a Gaussian random process. The idea is then to choose the next evaluation points using a probabilistic criterion that indicates, conditional on the previous evaluations, the most interesting regions of the research domain for the optimizer. Two difficulties in this approach can be identified: the choice of the Gaussian process prior and the maximization of the criterion. The first problem is usually solved by using a maximum likelihood approach, which turns out to be a poorly robust method, and to which we prefer a fully Bayesian approach. The contribution of this work is the introduction of a new Bayesian optimization algorithm, which maximizes the Expected Improvement (EI) criterion, and provides an answer to both problems thanks to a Sequential Monte Carlo approach. Numerical results on benchmark tests show good performances of our algorithm compared to those of several other methods of the literature.