  Importance sampling (IS) is a powerful Monte Carlo methodology for the
approximation of intractable integrals, very often involving a target
probability density function. The performance of IS heavily depends on the
appropriate selection of the proposal distributions where the samples are
simulated from. In this paper, we propose an adaptive importance sampler,
called GRAMIS, that iteratively improves the set of proposals. The algorithm
exploits geometric information of the target to adapt the location and scale
parameters of those proposals. Moreover, in order to allow for a cooperative
adaptation, a repulsion term is introduced that favors a coordinated
exploration of the state space. This translates into a more diverse exploration
and a better approximation of the target via the mixture of proposals.
Moreover, we provide a theoretical justification of the repulsion term. We show
the good performance of GRAMIS in two problems where the target has a
challenging shape and cannot be easily approximated by a standard uni-modal
proposal.
