发表机构
Georgia Institute of Technology（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对初始分布偏移问题，提出分布鲁棒薛定谔桥（DRSB），通过最小化最坏情况目标学习单一控制器，实验证明其鲁棒性优于标准SB。
AI 中文摘要
薛定谔桥（SB）学习在给定的初始分布和目标分布之间进行随机传输。当初始分布在测试时发生偏移，学习到的动力学可能无法恢复目标分布。我们提出了分布鲁棒薛定谔桥（DRSB），它学习一个单一的控制器，以考虑初始分布中的不确定性。DRSB目标由控制能量和最终终端分布与目标分布之间的KL惩罚组成。DRSB寻求一个单一控制器，在初始分布在名义分布周围的模糊集内变化时，最小化该目标的最坏情况值。我们推导了该目标的精确变分公式，并将其固定终端代价子问题与随机最优控制和分布鲁棒优化联系起来。该公式启发了一种交替算法，该算法更新对抗性初始分布，估计终端对数密度比，并训练控制器。我们利用随机控制最优性条件开发了Wasserstein和Sinkhorn变体，以近似对抗性更新所需的梯度。在二维传输任务和图像到图像翻译上的实验表明，相对于标准SB，对输入扰动的鲁棒性有所提高，但在名义性能上有所权衡。在高斯混合传输中，Sinkhorn DRSB在两种测试的未见噪声水平下，也实现了比固定水平噪声增强更低的平均切片Wasserstein距离。
英文摘要
Schrödinger bridge (SB) learns stochastic transport between prescribed initial and target distributions. When the initial distribution shifts at test time, the learned dynamics can fail to recover the target distribution. We introduce the Distributionally Robust Schrödinger Bridge (DRSB), which learns a single controller that accounts for uncertainty in the initial distribution. The DRSB objective consists of control energy and a KL penalty between the resulting terminal distribution and the target distribution. DRSB seeks a single controller that minimizes the worst-case value of this objective as the initial distribution varies within an ambiguity set around the nominal distribution. We derive an exact variational formulation of this objective and connect its fixed-terminal-cost subproblem to stochastic optimal control and distributionally robust optimization. This formulation motivates an alternating algorithm that updates the adversarial initial distribution, estimates the terminal log-density ratio, and trains the controller. We develop Wasserstein and Sinkhorn variants using stochastic control optimality conditions to approximate the gradients required for adversarial updates. Experiments on two-dimensional transport tasks and image-to-image translation show improved robustness to input perturbations relative to standard SB, with a tradeoff in nominal performance. On Gaussian mixture transport, Sinkhorn DRSB also achieves lower mean sliced Wasserstein distance than fixed-level noise augmentation at both tested unseen noise levels.
Comments30 pages, 5 figures
