Tractable Relaxations of Multivariate Stochastic Dominance via Optimal Transport and CVaR

What the math gives to ML

The paper turns multivariate stochastic dominance into a coupling feasibility condition that tolerates coordinatewise violations when they are compensated by sufficiently large improvements elsewhere. Its transferable asset is the asymmetric, transport-based margin: instead of matching samples by Euclidean distance, a model can be trained so that one output distribution dominates another under a user-specified weighted tradeoff. This yields a differentiable distribution-level regularizer for multi-attribute prediction, generative modeling, or preference alignment, with an interpretable tolerance parameter \(\gamma\) and attribute weights \(\beta_i\). The first implementation should use entropic optimal transport on minibatch outputs and penalize the smallest compensated-dominance violation.