BDRS：GPU 加速的离散最优传输新算法
GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport
一组 GPU 最优传输求解器 BDRS，支持代价矩阵、点云、网格三种输入，和 8 个现有 GPU 求解器同卡对比后跑出了更好成绩，做 OT 的可以看看实现。
论文提出 Bregman Douglas-Rachford splitting（BDRS）算法，用于在 GPU 上求解离散最优传输问题。BDRS 支持三种输入格式：显式代价矩阵、带地面代价的点云、规则网格上的可分离代价。针对每种格式，作者设计了硬件感知的等价表示以提升数值稳定性和运行速度。团队在同一设备上与文献中 8 个 GPU 基线求解器对比，三种实现均在各自格式上达到 SOTA，据称是首个使用统一最优性度量的 GPU DOT 跨求解器评测。
GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport
We present GPU-accelerated Bregman Douglas--Rachford splitting algorithm (BDRS) for discrete optimal transport problem in three input formats: an explicit cost matrix, a point cloud with a ground cost between them, and a separable cost on a regular grid. For each input format, we propose hardware-aware designs of mathematically equivalent representations for the BDRS iterations to enhance numerical stability and empirical runtime. We benchmark the three proposed implementations against eight GPU baseline solvers from the literature on the same device. We demonstrate that our implementations of BDRS achieve state-of-the-art performance on their respective input formats. To the best of our knowledge, this is the first cross-solver study of GPU DOT solvers with a unified measure of optimality.
