Distributionally Robust Optimization with Correlated Data from Vector Autoregressive Processes

TL;DR

This paper develops a distributionally robust optimization framework for non-i.i.d. vector autoregressive data using Wasserstein distance, transforming the problem into a convex-concave saddle point formulation and demonstrating its effectiveness on synthetic and real datasets.

Contribution

It introduces a novel robust optimization approach tailored for correlated time series data modeled by vector autoregressive processes, leveraging Wasserstein distance and duality theory.

Findings

The method is effective on synthetic data.

It performs well on real-world datasets.

The problem reduces to a convex-concave saddle point formulation.

Abstract

We present a distributionally robust formulation of a stochastic optimization problem for non-i.i.d vector autoregressive data. We use the Wasserstein distance to define robustness in the space of distributions and we show, using duality theory, that the problem is equivalent to a finite convex-concave saddle point problem. The performance of the method is demonstrated on both synthetic and real data.