Entropic Mirror Monte Carlo

TL;DR

This paper introduces an adaptive importance sampling method that enhances exploration of complex, high-dimensional distributions by combining global sampling with a novel delayed weighting scheme, leading to efficient and rapidly converging Monte Carlo estimations.

Contribution

The paper presents a new adaptive scheme for importance sampling that improves proposal distribution construction using delayed weighting and global exploration, with proven geometric convergence.

Findings

Algorithm demonstrates rapid convergence in numerical experiments.

Enhanced exploration in multimodal, high-dimensional distributions.

Improved efficiency over traditional importance sampling methods.

Abstract

Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions in highdimensional spaces, the efficiency of importance sampling critically depends on the choice of the proposal distribution. In this paper, we propose a novel adaptive scheme for the construction of efficient proposal distributions. Our algorithm promotes efficient exploration of the target distribution by combining global sampling mechanisms with a delayed weighting procedure. The proposed weighting mechanism plays a key role by enabling rapid resampling in regions where the proposal distribution is poorly adapted to the target. Our sampling algorithm is shown to be geometrically convergent under mild assumptions and is illustrated through various numerical experiments.