Emmanuel VAZQUEZ

Prof. & researcher in Bayesian design and analysis of computer experiments; coordinator of Data Science projects at CentraleSupelec

emmanuel.vazquez@l2s.centralesupelec.fr

L2S, CentraleSupélec

3 rue Joliot Curie

91190 Gif-sur-Yvette, France

*Design and analysis of computer experiments* is about using statistical approaches to problems such as approximation, uncertainty quantification, optimization… involving computer programs that emulate physical systems (see, e.g., Santner 2003).

My work relies on the theory of Bayesian sequential decision. In the domain of computer experiments, the Bayesian approach starts with a prior distribution that represents our prior belief about the structure of the computer model (see, e.g., the seminal article by Sacks et al. 1989). Most often, prior distributions for modeling computer models are derived from Gaussian processes (GP). The use of GP models has become a well-established framework beyond the domain of computer experiments (see, e.g., C.E. Rassmussen & C.K.I Williams 2006, Gaussian processes for ML).

By 2006, I suggested using a sequential approach for the estimation of the volume of excursion of a function above a threshold. This problem finds a direct application to the estimation of a probability of failure of a system. This work was the first instance of a SUR algorithm, which was improved and published during the period 2009–2013. See, for instance, Bect et al. 2011, Sequential design of computer experiments for the estimation of a probability of failure.

The consistency of several SUR strategies has been proved by Bect et al 2018.

How to optimize the performance of a system using numerical simulations? In particular, when simulations are time-consuming, it becomes essential to consider optimization algorithms that use the information provided by the simulations as efficiently as possible. Several approaches may be used. Most of them are based on the construction of an approximation of the output of the simulation (a metamodel). For instance, the idea of the Bayesian approach for optimization is to use a random process as a model of the function to be optimized. Then, the optimization is performed by making evaluations of the function in sequence, each evaluation being chosen in order to minimize a criterion that quantifies the expected loss, under the random process model, incurred by taking the best evaluation result collected so far instead of the true unknown optimum. Both theoretical and practical aspects are considered in my work, e.g.:

- An informational approach to the global optimization of expensive-to-evaluate functions in 2008
- Convergence properties of the expected improvement algorithm with fixed mean and covariance functions in 2010
- Robust Gaussian Process-Based Global Optimization Using a Fully Bayesian Expected Improvement Criterion in 2011
- A Bayesian approach to constrained single- and multi-objective optimization in 2017
- …