For McKean-Vlasov SDEs, the derivative of the distributionally robust value at zero perturbation is the L2 norm of an adjoint tangent-flow operator applied to the L-derivative of the objective.
Quantifying distributional m odel risk via optimal transport
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Sensitivity of functionals of McKean-Vlasov SDE's with respect to the initial distribution
For McKean-Vlasov SDEs, the derivative of the distributionally robust value at zero perturbation is the L2 norm of an adjoint tangent-flow operator applied to the L-derivative of the objective.