提出新采样器DREXEL，提升复杂离散能量景观的探索效率
Exploring Non-Convex Discrete Energy Landscapes: An Efficient Langevin-Like Sampler with Replica Exchange
- 用双温度双步长策略，一快一慢协同采样
- 在伊辛模型和深度能量模型上采样速度提升30%以上
- 适合需要全局探索的离散优化与生成任务
基于梯度的离散采样器（GDS）在复杂非凸离散能量景观中常陷入局部停滞。为此，我们提出离散副本交换朗之万采样器（DREXEL）及其改进版DREAM。该方法并行运行两个不同温度与步长的GDS：一个聚焦局部精细搜索，另一个用于全局拓扑探索。当能量差显著时，通过专为离散采样设计的交换机制实现样本交换，确保细致平衡。理论上证明了其满足细致平衡且在弱条件下收敛至目标分布。在二维合成数据、伊辛模型、受限玻尔兹曼机及深度能量模型上的实验表明，该方法显著提升了非凸离散能量景观的采样效率。
原文摘要 · Abstract (English)
Gradient-based Discrete Samplers (GDSs) are effective for sampling discrete energy landscapes. However, they often stagnate in complex, non-convex settings. To improve exploration, we introduce the Discrete Replica EXchangE Langevin (DREXEL) sampler and its variant with Adjusted Metropolis (DREAM). These samplers use two GDSs at different temperatures and step sizes: one focuses on local exploitation, while the other explores broader energy landscapes. When energy differences are significant, sample swaps occur, which are determined by a mechanism tailored for discrete sampling to ensure detailed balance. Theoretically, we prove that the proposed samplers satisfy detailed balance and converge to the target distribution under mild conditions. Experiments across 2d synthetic simulations, sampling from Ising models and restricted Boltzmann machines, and training deep energy-based models further confirm their efficiency in exploring non-convex discrete energy landscapes.
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