Log-Averaged Mirror Prox for Fast, Large-Scale Optimal Transport in Linear Space
We propose Log-Averaged Mirror Prox (LAMP), a linear-space primal-dual method for large-scale optimal transport. LAMP implements primal mirror prox updates by tracking an averaged dual sequence, reducing storage complexity from \({O}(nm)\) to \({O}(n+m)\) while preserving dense, GPU-friendly reductions. Consequently, LAMP preserves the last-iterate \(\widetilde{{O}}( nm\varepsilon^{-1})\) arithmetic complexity of conservatively parameterized primal-dual mirror prox. We further … Read more