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：本文研究了基于时间数据的期望函数值的分布鲁棒评估。一组备选的度量标准由因果最优传输所刻画。我们证明了强对偶性，并将因果约束重新构建为在无穷维测试函数空间内进行的最小化。我们通过神经网络近似测试函数，并证明了Rademacher复杂度下的样本复杂度。此外，当有结构信息可用于进一步限制歧义集时，我们证明了对偶公式，并提供了有效的优化方法。对实现波动率和股指的经验分析表明，我们的框架提供了经典最优传输公式的一种有吸引力的替代方案。