cs.AI updates on arXiv.org 07月24日 13:31
HOTA: Hamiltonian framework for Optimal Transport Advection
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本文提出了一种基于Hamilton-Jacobi-Bellman方程的Hamiltonian Optimal Transport Advection(HOTA)方法,通过Kantorovich势显式地解决双动态最优传输问题,实现高效且可扩展的轨迹优化,避免了显式密度建模的需求,在非光滑成本函数的情况下仍能表现优异。

arXiv:2507.17513v1 Announce Type: cross Abstract: Optimal transport (OT) has become a natural framework for guiding the probability flows. Yet, the majority of recent generative models assume trivial geometry (e.g., Euclidean) and rely on strong density-estimation assumptions, yielding trajectories that do not respect the true principles of optimality in the underlying manifold. We present Hamiltonian Optimal Transport Advection (HOTA), a Hamilton-Jacobi-Bellman based method that tackles the dual dynamical OT problem explicitly through Kantorovich potentials, enabling efficient and scalable trajectory optimization. Our approach effectively evades the need for explicit density modeling, performing even when the cost functionals are non-smooth. Empirically, HOTA outperforms all baselines in standard benchmarks, as well as in custom datasets with non-differentiable costs, both in terms of feasibility and optimality.

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HOTA 轨迹优化 最优传输 Hamilton-Jacobi-Bellman 密度估计
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