Convergence Analysis of the Sinkhorn Algorithm with Sparse Cost Matrices

This paper presents a theoretical analysis of the convergence rate of the Sinkhorn algorithm when the cost matrix is sparse. We derive bounds on the convergence rate that depend on the sparsity pattern and the degree of sparsity of the cost matrix. We also explore whether existing convergence results for dense cost matrices can be adapted or improved for the sparse case. Our analysis provides new insights into the behavior of the Sinkhorn algorithm in the presence of sparsity and highlights potential avenues for algorithmic improvements.