通过最小化增量KL散度，高效优化SMC采样器的马尔可夫核参数。
Tuning Sequential Monte Carlo Samplers via Greedy Incremental Divergence Minimization
- 以增量KL散度为优化目标，无需梯度即可调参
- 仅需几次标准SMC运行，即完成整套参数调优
- 适用于Langevin及动力学LMC等多种核方法
序列蒙特卡洛（SMC）采样器的性能高度依赖路径提议中马尔可夫核的调参。对于使用未调整马尔可夫核的SMC，传统的调参目标如MH接受率或期望平方跳跃距离已不再适用。尽管已有基于随机梯度的端到端优化方法用于调参，但通常训练成本过高，即使仅调核步长也如此。本文提出一种通用自适应框架，通过最小化提议路径与目标路径间的增量Kullback-Leibler（KL）散度来调参。针对步长调参，我们提供了一种无需梯度、无需调参的算法，适用于Langevin Monte Carlo（LMC）等核。进一步地，我们为用于SMC中的动力学LMC设计了定制化调参方案。实现表明，仅需少量标准SMC运行，即可获得完整参数调度，计算成本远低于基于梯度的方法。
原文摘要 · Abstract (English)
The performance of sequential Monte Carlo (SMC) samplers heavily depends on the tuning of the Markov kernels used in the path proposal. For SMC samplers with unadjusted Markov kernels, standard tuning objectives, such as the Metropolis-Hastings acceptance rate or the expected-squared jump distance, are no longer applicable. While stochastic gradient-based end-to-end optimization has been explored for tuning SMC samplers, they often incur excessive training costs, even for tuning just the kernel step sizes. In this work, we propose a general adaptation framework for tuning the Markov kernels in SMC samplers by minimizing the incremental Kullback-Leibler (KL) divergence between the proposal and target paths. For step size tuning, we provide a gradient- and tuning-free algorithm that is generally applicable for kernels such as Langevin Monte Carlo (LMC). We further demonstrate the utility of our approach by providing a tailored scheme for tuning kinetic LMC used in SMC samplers. Our implementations are able to obtain a full schedule of tuned parameters at the cost of a few vanilla SMC runs, which is a fraction of gradient-based approaches.
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