arXiv 2602.212722026-02-24stat.MLcs.LGstat.CO

反 diagonal 霍尔顿采样

Counterdiabatic Hamiltonian Monte Carlo

University of California, Berkeley（加州大学伯克利分校）；New York University（纽约大学）

Reuben Cohn-Gordon, Uroš Seljak, Dries Sels

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AI总结：

反 diagonal 霍尔顿采样通过引入学习的反 diagonal 项，提高多模问题的采样效率，适用于复杂分布的高效采样。

摘要：

霍尔顿采样（HMC）是一种用于从可微密度分布中采样的前沿方法，但在应用于具有挑战性的多模问题时会收敛缓慢。运行具有时间变化霍尔顿的霍尔顿，以从初始可处理分布插值到目标分布，可以解决这个问题。结合一种消除了偏差的加权方案，这可以被视为顺序蒙特卡洛（SMC）采样的一种特殊情况。然而，这种方法可能效率低下，因为它需要在初始和最终分布之间缓慢变化。受Sels等人（2017）的启发，其中在霍尔顿中添加一个学习的反 diagonal 项允许高效地准备量子态，我们提出了反 diagonal 霍尔顿采样（CHMC），可以视为具有更高效内核的SMC采样器。我们建立了它与最近用于加速基于梯度的采样方法的提议之间的关系，并在简单的基准问题上进行了演示。

英文摘要：

Hamiltonian Monte Carlo (HMC) is a state of the art method for sampling from distributions with differentiable densities, but can converge slowly when applied to challenging multimodal problems. Running HMC with a time varying Hamiltonian, in order to interpolate from an initial tractable distribution to the target of interest, can address this problem. In conjunction with a weighting scheme to eliminate bias, this can be viewed as a special case of Sequential Monte Carlo (SMC) sampling \cite{doucet2001introduction}. However, this approach can be inefficient, since it requires slow change between the initial and final distribution. Inspired by \cite{sels2017minimizing}, where a learned \emph{counterdiabatic} term added to the Hamiltonian allows for efficient quantum state preparation, we propose \emph{Counterdiabatic Hamiltonian Monte Carlo} (CHMC), which can be viewed as an SMC sampler with a more efficient kernel. We establish its relationship to recent proposals for accelerating gradient-based sampling with learned drift terms, and demonstrate on simple benchmark problems.

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