Optimal Transport with Adaptive Regularisation

TL;DR

This paper introduces OTARI, a new optimal transport formulation with adaptive regularisation that imposes local constraints on mass transfer, improving control over smoothing and distribution in applications like domain adaptation.

Contribution

The paper proposes OTARI, a novel optimal transport method with local constraints, addressing limitations of global regularisation and enhancing application-specific control.

Findings

OTARI improves mass distribution control in optimal transport.

OTARI enhances domain adaptation performance.

Adaptive regularisation reduces smoothing imbalance.

Abstract

Regularising the primal formulation of optimal transport (OT) with a strictly convex term leads to enhanced numerical complexity and a denser transport plan. Many formulations impose a global constraint on the transport plan, for instance by relying on entropic regularisation. As it is more expensive to diffuse mass for outlier points compared to central ones, this typically results in a significant imbalance in the way mass is spread across the points. This can be detrimental for some applications where a minimum of smoothing is required per point. To remedy this, we introduce OT with Adaptive RegularIsation (OTARI), a new formulation of OT that imposes constraints on the mass going in or/and out of each point. We then showcase the benefits of this approach for domain adaptation.