Robust Quasi Monte Carlo

Résumé : Given a simulation budget of N points to calculate an expectation/integral, and some confidence level, what is the optimal confidence interval one can build? For which estimator? The classic Monte Carlo method builds intervals of size proportional to the inverse squared root of N and of the confidence level. Can we do better? The answer is yes. However, “standard” variance reduction techniques such as Quasi Monte Carlo are not fully efficient for this task. In this talk, we show that a judicious choice of “robust” aggregation methods coupled with Quasi Monte Carlo techniques allows reaching the optimal error bound. I will review Quasi Monte Carlo methods, different concentration inequalities and robust mean estimators (old and new) to get to the solution, with supporting numerical experiments. I will end by showing how this research makes sense at INRAE 🐑🐑🐑 This is a joint work with M. Lerasle and E. Gobet.