  This survey gives an overview of Monte Carlo methodologies using surrogate
models, for dealing with densities which are intractable, costly, and/or noisy.
This type of problem can be found in numerous real-world scenarios, including
stochastic optimization and reinforcement learning, where each evaluation of a
density function may incur some computationally-expensive or even physical
(real-world activity) cost, likely to give different results each time. The
surrogate model does not incur this cost, but there are important trade-offs
and considerations involved in the choice and design of such methodologies. We
classify the different methodologies into three main classes and describe
specific instances of algorithms under a unified notation. A modular scheme
which encompasses the considered methods is also presented. A range of
application scenarios is discussed, with special attention to the
likelihood-free setting and reinforcement learning. Several numerical
comparisons are also provided.
