On the optimization of approximate control variates with parametrically defined estimators

Multi-model Monte Carlo methods, such as multi-level (MLMC) and multifidelity (MFMC), allow for efficient estimation of the expectation a quantity interest given set models varying fidelities. Recently, it was shown that MLMC MFMC estimators are both instances approximate control variates (ACV) framework [Gorodetsky et al. (2020) [14]]. In same work, also hand-tailored ACV could outperform variety model scenarios. Because there is no reason to believe these best among myriad possible estimators, more general approach estimator construction pursued in this work. First, form variance formulated. Then, formulation utilized generate parametrically-defined estimators. These an optimization be over larger domain The tested on large scenarios, found broader search enabled by leads greater reduction.