We introduce a new class of adaptive importance samplers leveraging adaptive optimisation tools, which we term AdaOAIS. We build on Optimised Adaptive Importance Samplers (OAIS), a class of techniques that adapt proposals to improve the mean-squared error of the importance sampling estimators by parameterising the proposal and optimising the $\chi^2$-divergence between the target and the proposal. We show that a naive implementation of OAIS using stochastic gradient descent may lead to unstable estimators despite its convergence guarantees. To remedy this shortcoming, we instead propose to use adaptive optimisers (such as AdaGrad and Adam) to improve the stability of the OAIS. We provide convergence results for AdaOAIS in a similar manner to OAIS. We also provide empirical demonstration on a variety of examples and show that AdaOAIS lead to stable importance sampling estimators in practice.

翻译：我们提出了一类新的自适应重要性采样器，利用自适应优化工具，并将其命名为AdaOAIS。我们基于优化自适应重要性采样器（OAIS）——一类通过参数化提议分布并优化目标分布与提议分布之间的$\chi^2$散度，以降低重要性采样估计器均方误差的技术。研究表明，使用随机梯度下降的朴素OAIS实现尽管具有收敛保证，但可能导致估计器不稳定。为解决这一缺陷，我们提出采用自适应优化器（如AdaGrad和Adam）来提升OAIS的稳定性。我们以与OAIS相似的方式给出了AdaOAIS的收敛性结果，并通过多个实例的实证证明，AdaOAIS在实际应用中能够获得稳定的重要性采样估计器。