Low-Rank Multimarginal Optimal Transport

Multimarginal Optimal Transport (MOT) suffers from exponential computational and memory costs in the number of marginals, as transport plans are represented by high-dimensional tensors. We introduce Low-Rank Multimarginal Optimal Transport (LRMOT), which restricts transport plans to tensors with bounded multilinear rank, providing a compact and structured representation of multimarginal couplings. This structure enables efficient algorithms with a low memory footprint. We establish approximation bounds for the resulting low-rank formulations and demonstrate experimentally that the proposed algorithms substantially reduce computational time while achieving solutions of good quality.