Rigorous stochastic treatment of SUDO and RUOT-like dynamics

Establish a rigorous theoretical formulation and analysis of stochastic dynamics for the SUDO framework and its regularized unbalanced optimal transport (RUOT)-like setting.

Background

The paper develops its theoretical formulation for deterministic UDOT, whose constraint is a continuity equation with a source term. It also presents an empirical stochastic extension for RUOT-like settings by replacing conditional unbalanced flow matching with conditional unbalanced score matching. However, the authors explicitly identify the absence of a rigorous treatment of these stochastic dynamics as an unresolved limitation.

References

First, while SUDO provides an empirical approach for RUOT-like settings, its theoretical formulation is currently developed for deterministic dynamics, leaving a rigorous treatment of stochastic dynamics for future work.

— Simulation-free Unbalanced Dynamic Optimal Transport with General Growth Penalty  (2609.04710 - Ying et al., 4 Sep 2026) in Section 6, “Conclusion”

Beyond categorising existing methods, we discuss the motivations behind different OT choices, practical considerations such as cost design and computational challenges, and highlight open problems including scalable trajectory-level transport, principled handling of mass mismatch, and theoretical analysis for OT-regularised RL.

— Optimal Transport Meets Reinforcement Learning: A Survey  (2610.01413 - Zhu et al., 1 Oct 2026) in Abstract