无需梯度计算即可高效探索多峰分布的采样新方法
Gradient-free Riemannian Langevin Sampler
- 通过黎曼度量重塑局部几何，促进跨峰转移
- 在多个多峰基准上混合速度优于现有梯度与无梯度方法
- 适合目标函数无梯度或计算昂贵的场景
针对多峰概率分布采样中标准马尔可夫链蒙特卡洛方法易出现混合缓慢和模式陷落的问题，本文提出无梯度黎曼 Langevin 采样器（GRiLS）。该方法不依赖目标密度的梯度信息，通过引入黎曼度量重塑局部几何，提升跨峰探索能力。算法需知目标分布的均值与协方差，通过一组相互作用粒子的集合进行估计。在多个多峰基准测试中，GRiLS 在混合性能上显著优于现有的梯度型与无梯度型 MCMC 方法。
原文摘要 · Abstract (English)
We address the problem of efficiently sampling multimodal probability distributions, where standard Markov Chain Monte Carlo methods often suffer from poor mixing and mode trapping. To mitigate these issues, we propose Gradient-free Riemannian Langevin Sampler (GRiLS), a novel proposal that improves exploration without requiring gradient evaluations of the target density. Our approach introduces a Riemannian metric which reshapes the local geometry in order to facilitate transitions across modes. The resulting gradient-free MCMC algorithm is particularly suitable for complex, computationally expensive targets where derivatives are unavailable or impractical. The GRiLS proposal requires knowing the mean and covariance of the target density, which we estimate using an ensemble of interacting particles. Empirical results on multimodal benchmarks demonstrate that GRiLS achieves improved mixing compared to existing gradient-based and gradient-free MCMC approaches.
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