This work studies distributionally robust evaluation of expected function values over temporal data. A set of alternative measures is characterized by the causal optimal transport. We prove the strong duality and recast the causality constraint as minimization over an infinite-dimensional test function space. We approximate test functions by neural networks and prove the sample complexity with Rademacher complexity. Moreover, when structural information is available to further restrict the ambiguity set, we prove the dual formulation and provide efficient optimization methods. Empirical analysis of realized volatility and stock indices demonstrates that our framework offers an attractive alternative to the classic optimal transport formulation.

翻译：本文研究时间序列数据上期望函数值的分布鲁棒评估。通过因果最优传输刻画了一组替代测度。我们证明了强对偶性，并将因果约束转化为无限维测试函数空间上的最小化问题。利用神经网络近似测试函数，并基于Rademacher复杂度证明了样本复杂度。此外，当利用结构信息进一步约束模糊集时，我们推导了对偶形式并提供了高效的优化方法。对已实现波动率和股票指数的实证分析表明，我们的框架为经典最优传输公式提供了一种有吸引力的替代方案。