Recurrent machines for likelihood-free inference

Likelihood-free inference is concerned with the estimation of the parameters of
a non-differentiable stochastic simulator that best reproduce real observations.
In the absence of a likelihood function, most of the existing inference methods
optimize the simulator parameters through a handcrafted iterative procedure that
tries to make the simulated data more similar to the observations. In this work,
we explore whether meta-learning can be used in the likelihood-free context, for
learning automatically from data an iterative optimization procedure that would
solve likelihood-free inference problems. We design a recurrent inference machine
that learns a sequence of parameter updates leading to good parameter estimates,
without ever specifying some explicit notion of divergence between the simulated
data and the real data distributions. We demonstrate our approach on toy simulators,
showing promising results both in terms of performance and robustness.