Gradients have been exploited in proposal distributions to accelerate the convergence of Markov chain Monte Carlo algorithms on discrete distributions. However, these methods require a natural differentiable extension of the target discrete distribution, which often does not exist or does not provide effective gradient guidance. In this paper, we develop a gradient-like proposal for any discrete distribution without this strong requirement. Built upon a locally-balanced proposal, our method efficiently approximates the discrete likelihood ratio via Newton's series expansion to enable a large and efficient exploration in discrete spaces. We show that our method can also be viewed as a multilinear extension, thus inheriting its desired properties. We prove that our method has a guaranteed convergence rate with or without the Metropolis-Hastings step. Furthermore, our method outperforms a number of popular alternatives in several different experiments, including the facility location problem, extractive text summarization, and image retrieval.

翻译：梯度已被用于提议分布中，以加速马尔可夫链蒙特卡洛算法在离散分布上的收敛性。然而，这些方法要求目标离散分布具有自然的可微扩展形式，而这通常不存在或无法提供有效的梯度引导。本文针对任意离散分布，在不依赖这一强条件的前提下，提出了一种类梯度提议方法。该方法基于局部平衡提议，通过牛顿级数展开高效近似离散似然比，从而实现在离散空间中的大规模高效探索。我们证明该方法也可视为多重线性扩展，因而继承了其理想性质。我们还证明，无论是否使用Metropolis-Hastings步骤，该方法均具有保证的收敛速率。此外，在包括设施选址问题、抽取式文本摘要和图像检索在内的多项实验中，我们的方法优于多种主流替代方案。