Non-reversible parallel tempering (NRPT) is an effective algorithm for sampling from target distributions with complex geometry, such as those arising from posterior distributions of weakly identifiable and high-dimensional Bayesian models. In this work we establish the uniform (geometric) ergodicity of NRPT under a model of efficient local exploration. The uniform ergodicity log rates are inversely proportional to an easily-estimable divergence, the global communication barrier (GCB), which was recently introduced in the literature. We obtain analogous ergodicity results for classical reversible parallel tempering, providing new evidence that NRPT dominates its reversible counterpart. Our results are based on an analysis of the hitting time of a continuous-time persistent random walk, which is also of independent interest. The rates that we obtain reflect real experiments well for distributions where global exploration is not possible without parallel tempering.

翻译：不可逆平行回火算法（NRPT）是一种从具有复杂几何结构的目标分布（例如弱可识别高维贝叶斯模型的后验分布）中进行采样的有效算法。本文在高效局部探索模型下，证明了NRPT的一致（几何）遍历性。该一致遍历性的对数速率与易于估计的散度——即近期文献中提出的全局通信屏障（GCB）——成反比。我们进一步获得了经典可逆平行回火算法的类似遍历性结果，为NRPT优于其可逆对应方法提供了新证据。我们的研究基于对连续时间持续随机游走击中时间的分析，这一分析本身亦具有独立价值。对于无法通过平行回火实现全局探索的分布，所得速率能较好地反映实际实验表现。