An efficient algorithm for entropic optimal transport under martingale-type constraints
Keywords: Optimal Transport, Martingale Constraints
Abstract: This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions.
The problems can map to a prevalent class of OT problems with structural constraints, encompassing the discrete martingale optimal transport (MOT) problem, as the (super-)martingale conditions are equivalent to row-wise (in-)equality constraints on the coupling matrix. Inspired by the recent empirical success of Sinkhorn-type algorithms, we propose an entropic formulation for the MOT problem and introduce Sinkhorn-type algorithms with sparse Newton iterations that utilize the (approximate) sparsity of the Hessian matrix of the dual objective. As exact martingale conditions are typically infeasible, we adopt entropic regularization to find an approximate constraint satisfied solution. We show that in practice the proposed algorithms enjoy both super-exponential convergence and robustness with controllable thresholds for total constraint violations.
Primary Area: optimization
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Submission Number: 5323
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