Stability of Wasserstein projections in convex order via metric extrapolation

TL;DR

This paper establishes new stability estimates for Wasserstein projections in convex order by connecting recent work on projections and metric extrapolation, enhancing understanding of their robustness.

Contribution

It introduces novel quantitative stability estimates for Wasserstein projections in convex order through the application of metric extrapolation techniques.

Findings

Derived stability bounds for Wasserstein projections in convex order.

Linked backward and forward W2-projections with metric extrapolation.

Enhanced understanding of the robustness of Wasserstein projections.

Abstract

We build on recent work linking backward and forward W2-projections in convex order with the recently introduced metric extrapolation problem to derive new quantitative stability estimates for both problems.