无需梯度信息的新型采样方法，实现快速收敛。
Alternating Diffusion for Proximal Sampling with Zeroth Order Queries
- 基于零阶信息构建近端采样器，通过粒子分布模拟得分估计。
- 在目标分布满足等周条件下，理论证明指数级收敛。
- 避免拒绝采样，支持灵活步长，适合并行计算场景。
本文提出一种仅依赖势函数零阶信息的近端采样新方法。已有理论表明，近端采样对应热流的交替前向与后向迭代，其中后向步骤原由拒绝采样实现，而本文直接模拟其动力学过程。不同于依赖学习模型或辅助采样的扩散采样方法，本方法将中间粒子分布视为高斯混合，从而从可直接采样的分布中获得蒙特卡洛得分估计器。理论上，当得分估计误差足够受控时，该方法在目标分布满足等周条件下继承近端采样的指数收敛性。实践中，算法避免了拒绝采样，支持灵活步长，并具有确定的运行时间预算。数值实验表明，该方法通过多粒子间相互作用及并行计算，快速收敛至目标分布。
原文摘要 · Abstract (English)
This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and backward iterations of the heat flow. The backward step was originally implemented by rejection sampling, whereas we directly simulate the dynamics. Unlike diffusion-based sampling methods that estimate scores via learned models or by invoking auxiliary samplers, our method treats the intermediate particle distribution as a Gaussian mixture, thereby yielding a Monte Carlo score estimator from directly samplable distributions. Theoretically, when the score estimation error is sufficiently controlled, our method inherits the exponential convergence of proximal sampling under isoperimetric conditions on the target distribution. In practice, the algorithm avoids rejection sampling, permits flexible step sizes, and runs with a deterministic runtime budget. Numerical experiments demonstrate that our approach converges rapidly to the target distribution, driven by interactions among multiple particles and by exploiting parallel computation.
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