Hamiltonian Monte Carlo (HMC) is a widely used sampler for continuous probability distributions. In many cases, the underlying Hamiltonian dynamics exhibit a phenomenon of resonance which decreases the efficiency of the algorithm and makes it very sensitive to hyperparameter values. This issue can be tackled efficiently, either via the use of trajectory length randomization (RHMC) or via partial momentum refreshment. The second approach is connected to the kinetic Langevin diffusion, and has been mostly investigated through the use of Generalized HMC (GHMC). However, GHMC induces momentum flips upon rejections causing the sampler to backtrack and waste computational resources. In this work we focus on a recent algorithm bypassing this issue, named Metropolis Adjusted Langevin Trajectories (MALT). We build upon recent strategies for tuning the hyperparameters of RHMC which target a bound on the Effective Sample Size (ESS) and adapt it to MALT, thereby enabling the first user-friendly deployment of this algorithm. We construct a method to optimize a sharper bound on the ESS and reduce the estimator variance. Easily compatible with parallel implementation, the resultant Adaptive MALT algorithm is competitive in terms of ESS rate and hits useful tradeoffs in memory usage when compared to GHMC, RHMC and NUTS.

翻译：哈密顿蒙特卡洛（HMC）是连续概率分布中广泛使用的采样器。在许多情况下，底层哈密顿动力学表现出共振现象，这会降低算法效率并使其对超参数值极为敏感。该问题可通过轨迹长度随机化（RHMC）或部分动量刷新有效解决。第二种方法与动力学Langevin扩散相关，主要通过广义HMC（GHMC）进行研究。然而，GHMC在拒绝时会导致动量翻转，使采样器回溯并浪费计算资源。本文聚焦于一种新近提出的规避该问题的算法——Metropolis调整Langevin轨迹（MALT）。我们基于近期针对RHMC超参数调优的策略（以有效样本量（ESS）上界为目标），将其适配至MALT，从而首次实现该算法的用户友好部署。我们构建了一种方法以优化ESS的更紧上界并降低估计器方差。该方法易于并行实现，由此产生的自适应MALT算法在ESS速率方面具有竞争力，并在内存使用上与GHMC、RHMC及NUTS相比实现了有益的权衡。