Self-learning Monte Carlo (SLMC) methods are recently proposed to accelerate Markov chain Monte Carlo (MCMC) methods using a machine learning model. With latent generative models, SLMC methods realize efficient Monte Carlo updates with less autocorrelation. However, SLMC methods are difficult to directly apply to multimodal distributions for which training data are difficult to obtain. To solve the limitation, we propose parallel adaptive annealing, which makes SLMC methods directly apply to multimodal distributions with a gradually trained proposal while annealing target distribution. Parallel adaptive annealing is based on (i) sequential learning with annealing to inherit and update the model parameters, (ii) adaptive annealing to automatically detect under-learning, and (iii) parallel annealing to mitigate mode collapse of proposal models. We also propose VAE-SLMC method which utilizes a variational autoencoder (VAE) as a proposal of SLMC to make efficient parallel proposals independent of any previous state using recently clarified quantitative properties of VAE. Experiments validate that our method can proficiently obtain accurate samples from multiple multimodal toy distributions and practical multimodal posterior distributions, which is difficult to achieve with the existing SLMC methods.

翻译：自我学习蒙特卡洛（SLMC）方法近期被提出用于加速马尔可夫链蒙特卡洛（MCMC）方法，其通过引入机器学习模型实现。利用潜在生成模型，SLMC方法能以较低的自相关性实现高效的蒙特卡洛更新。然而，SLMC方法难以直接应用于训练数据难以获取的多峰分布。为解决这一局限，我们提出并行自适应退火方法，通过逐步训练提议分布并在退火过程中自适应调整目标分布，使SLMC方法可直接适用于多峰分布。并行自适应退火基于以下机制：（i）通过退火实现序贯学习以继承并更新模型参数；（ii）通过自适应退火自动检测欠学习状态；（iii）通过并行退火缓解提议分布的模式坍塌问题。此外，我们提出VAE-SLMC方法，利用变分自编码器（VAE）作为SLMC的提议分布，结合近期阐明的VAE定量特性，生成独立于先前状态的高效并行提议。实验验证表明，我们的方法能够从多个多峰玩具分布及实际多峰后验分布中高效获取精确样本，而现有SLMC方法难以实现这一效果。