arXiv:2508.02770cs.ITcs.LG2025-08被引 2
首次证明IMF算法在有限状态空间下呈指数收敛。
Exponential convergence rate for Iterative Markovian Fitting
- 提出显式收缩因子，量化IMF的收敛速度。
- 证明IMF在KL散度下以指数速率收敛。
- 为随机路径生成提供理论保障，适合算法研究者。
我们研究有限状态空间上的离散时间Schrödinger桥问题。尽管已知迭代马尔可夫拟合（IMF）算法在KL散度下收敛于真实解，但其收敛速度未被量化。本文首次建立IMF具有显式收缩因子的指数收敛性，为该算法的高效性提供了理论依据。
原文摘要 · Abstract (English)
We consider the discrete-time Schrödinger bridge problem on a finite state space. Although it has been known that the Iterative Markovian Fitting (IMF) algorithm converges in Kullback-Leibler divergence to the ground truth solution, the speed of that convergence remained unquantified. In this work, we establish for the first time that IMF exhibits exponential convergence with an explicit contraction factor.
优化概率推断收敛分析
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