论文标题
在未经调整的凸光外壳中，HMC和阻尼不足的Langevin United
HMC and underdamped Langevin united in the unadjusted convex smooth case
论文作者
论文摘要
我们考虑了一个未经调整的HMC采样器的家族，其中包括标准位置HMC采样器和失业不足的Langevin工艺的离散化。在高斯案例中进行了详细的分析和优化参数，该案例显示，通过使用部分速度刷新的条件数量$κ$，收敛速度从$ 1/κ$提高到$ 1/\sqrtκ$，就经典的完整刷新而言。对于两种相关算法，即大都市调整后的GHMC和动力学分段确定的马尔可夫过程，也观察到类似的效果。然后，考虑了采样器的随机梯度版本，为此，在大量参数上建立了对数孔的平滑目标的无维度的收敛速率，在统一的框架中收集了先前的框架上的结果HMC和阻尼不足的Langevin，并将其扩展到HMC与HMC扩展到HMC。
We consider a family of unadjusted generalized HMC samplers, which includes standard position HMC samplers and discretizations of the underdamped Langevin process. A detailed analysis and optimization of the parameters is conducted in the Gaussian case, which shows an improvement from $1/κ$ to $1/\sqrtκ$ for the convergence rate in terms of the condition number $κ$ by using partial velocity refreshment, with respect to classical full refreshments. A similar effect is observed empirically for two related algorithms, namely Metropolis-adjusted gHMC and kinetic piecewise-deterministic Markov processes. Then, a stochastic gradient version of the samplers is considered, for which dimension-free convergence rates are established for log-concave smooth targets over a large range of parameters, gathering in a unified framework previous results on position HMC and underdamped Langevin and extending them to HMC with inertia.
