[2210.10785] gradient-based adaptive importance sampler

[Submitted on 19 Oct 2022]

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Overview: Importance sampling (IS) is a powerful Monte Carlo method for approximating intractable integrals, often involving target probability distributions. The performance of IS is highly dependent on a good choice of proposal distribution for which the samples are simulated. In this paper, we propose an adaptive importance sampler called GRAMIS that iteratively improves a set of suggestions. The algorithm utilizes the target’s geometric information to adapt the position and scale parameters of these proposals. Furthermore, a repulsion term is introduced that favors a coordinated search of the state space to enable cooperative adaptation. This leads to more diverse investigations and a better approximation of targets through a mixture of suggestions. Furthermore, we provide a theoretical justification for the repulsion term. We demonstrate the excellent performance of GRAMIS on two problems whose targets have challenging geometries and are not easily approximated by standard single-mode proposals.