Screening Sinkhorn Algorithm for Regularized Optimal Transport
This work addresses computational bottlenecks in optimal transport for machine learning practitioners, offering an incremental improvement over existing Sinkhorn-based methods.
The authors tackled the computational inefficiency of approximating Sinkhorn distances in regularized optimal transport by introducing the Screenkhorn algorithm, which screens neglectable dual components to solve a smaller problem with provable guarantees, achieving significant speed-ups in tasks like dimensionality reduction and domain adaptation.
We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to screen those components by directly setting them at that value before entering the Sinkhorn problem. This allows us to solve a smaller Sinkhorn problem while ensuring approximation with provable guarantees. More formally, the approach is based on a new formulation of dual of Sinkhorn divergence problem and on the KKT optimality conditions of this problem, which enable identification of dual components to be screened. This new analysis leads to the Screenkhorn algorithm. We illustrate the efficiency of Screenkhorn on complex tasks such as dimensionality reduction and domain adaptation involving regularized optimal transport.