提出新型稳定算法，提升量子桥模型在不确定数据下的学习鲁棒性。
Variational Online Mirror Descent for Robust Learning in Schrödinger Bridge
- 基于变分在线镜像下降框架，增强量子桥求解稳定性。
- 理论证明算法收敛且具有可保证的后悔界，实验性能优于现有方法。
- 适合追求高鲁棒性生成模型的科研与工程人员参考。
量子桥（Schrödinger Bridge, SB）已成为通用的概率生成模型类别。然而，实践中估计的学习信号固有不确定性，现有方法承诺的可靠性往往依赖于理想化假设。近期关于通过镜像下降（MD）研究Sinkhorn算法的工作揭示了求解SB问题的几何洞察。本文提出一种用于SB问题的变分在线镜像下降（OMD）框架，进一步提升了SB求解器的稳定性。我们正式证明了该新型OMD公式的收敛性及后悔界。由此，我们提出无需模拟的量子桥算法——变分镜像量子桥（VMSB），利用高斯混合参数化下舒尔茨势能的Wasserstein-Fisher-Rao几何。基于Wasserstein梯度流理论，该算法提供了可计算的学习动态，精确逼近每一步OMD更新。实验表明，所提VMSB算法在广泛基准测试中持续优于当前主流的SB求解器，验证了其由OMD理论预测的鲁棒性与通用性。
原文摘要 · Abstract (English)
The Schrödinger bridge (SB) has evolved into a universal class of probabilistic generative models. In practice, however, estimated learning signals are innately uncertain, and the reliability promised by existing methods is often based on speculative optimal case scenarios. Recent studies regarding the Sinkhorn algorithm through mirror descent (MD) have gained attention, revealing geometric insights into solution acquisition of the SB problems. In this paper, we propose a variational online MD (OMD) framework for the SB problems, which provides further stability to SB solvers. We formally prove convergence and a regret bound for the novel OMD formulation of SB acquisition. As a result, we propose a simulation-free SB algorithm called Variational Mirrored Schrödinger Bridge (VMSB) by utilizing the Wasserstein-Fisher-Rao geometry of the Gaussian mixture parameterization for Schrödinger potentials. Based on the Wasserstein gradient flow theory, the algorithm offers tractable learning dynamics that precisely approximate each OMD step. In experiments, we validate the performance of the proposed VMSB algorithm across an extensive suite of benchmarks. VMSB consistently outperforms contemporary SB solvers on a wide range of SB problems, demonstrating the robustness as well as generality predicted by our OMD theory.
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