Generalization of the SOC surrogate beyond evaluated tasks and distributions

Establish whether the SOC gradient surrogate used by the Distributionally Robust Schrödinger Bridge adversarial updates is valid across tasks and input distributions beyond the evaluated two-dimensional Gaussian experiment.

Background

The adversarial update in the implemented method substitutes the value-function gradient with the negative controller drift. The paper evaluates this approximation only on a single two-dimensional Gaussian transport experiment and observes close agreement there.

The authors explicitly state that the experiment does not establish validity across other tasks and input distributions, leaving the broader applicability of this surrogate unresolved.

References

They do not establish exact SOC optimality or its validity across other tasks and input distributions.

— Distributionally Robust Schrödinger Bridge  (2610.02043 - Sul et al., 1 Oct 2026) in Appendix H, subsection “Empirical Check of the SOC Optimality Condition”