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

Efficient Informed Proposals for Discrete Distributions via Newton's Series Approximation