The accelerated weight histogram (AWH) algorithm is an iterative extended ensemble algorithm, developed for statistical physics and computational biology applications. It is used to estimate free energy differences and expectations with respect to Gibbs measures. The AWH algorithm is based on iterative updates of a design parameter, which is closely related to the free energy, obtained by matching a weight histogram with a specified target distribution. The weight histogram is constructed from samples of a Markov chain on the product of the state space and parameter space. In this paper almost sure convergence of the AWH algorithm is proved, for estimating free energy differences as well as estimating expectations with adaptive ergodic averages. The proof is based on identifying the AWH algorithm as a stochastic approximation and studying the properties of the associated limit ordinary differential equation.

翻译：加速重量直方图算法是一种为统计物理和计算生物学应用开发的迭代扩展混合算法,用于估算与Gibbs测量值有关的自由能源差异和预期值。AWh算法基于设计参数的迭代更新,该设计参数与自由能源密切相关,通过将重量直方图与特定目标分布相匹配而获得。权重直方法是用国家空间和参数空间产品的Markov链条样本和参数空间构建的。在本文中,几乎可以肯定地证明AWh算法的趋同性,以估计自由能源差异并估计与适应性垂直平均值的预期值。证据的依据是将AWh算法确定为随机近距离并研究相关限制普通差方的特性。