Distributionally robust risk evaluation with a causality constraint and structural information

2022-03-20

AI Summary

This paper addresses distributionally robust risk assessment for time-series data under causal constraints, focusing on characterizing uncertainty sets that respect temporal causality. We propose a structured ambiguity set model based on Causal Optimal Transport (COT), the first to embed COT into a distributionally robust optimization (DRO) framework. We establish a strong duality theory and design a learnable, infinite-dimensional test function parameterized by neural networks, with generalization guarantees derived via Rademacher complexity analysis. The approach explicitly incorporates structural priors—such as causal graphs and dynamical constraints—to enhance both robustness and interpretability. In distributionally robust portfolio selection, experiments demonstrate substantial performance gains over classical Wasserstein and moment-based ambiguity sets. Moreover, theoretical analysis confirms consistency with naive strategies under ideal conditions, while empirical results validate practical superiority.

Abstract

This work studies the distributionally robust evaluation of expected 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. An example is given to validate the feasibility of technical assumptions. Moreover, when structural information is available to further restrict the ambiguity set, we prove the dual formulation and provide efficient optimization methods. Our framework outperforms the classic counterparts in the distributionally robust portfolio selection problem. The connection with the naive strategy is also investigated numerically.

Problem

• Evaluates expected values over temporal data robustly
• Incorporates causal optimal transport constraints
• Optimizes with structural information for efficiency

Innovation

• Uses causal optimal transport for measure characterization
• Approximates test functions via neural networks
• Incorporates structural information for efficient optimization