A Data-Driven Approach to Multistage Stochastic Linear Optimization

We propose a new data-driven approach for addressing multistage stochastic linear optimization problems with unknown distributions. The approach consists of solving a robust optimization problem that is constructed from sample paths of the underlying stochastic process. We provide asymptotic bounds on the gap between the optimal costs of the robust optimization problem and the underlying stochastic problem as more sample paths are obtained, and we characterize cases in which this gap is equal to zero. To the best of our knowledge, this is the first sample path approach for multistage stochastic linear optimization that offers asymptotic optimality guarantees when uncertainty is arbitrarily correlated across time. Finally, we develop approximation algorithms for the proposed approach by extending techniques from the robust optimization literature and demonstrate their practical value through numerical experiments on stylized data-driven inventory management problems.

Automated summary

This paper proposes a new data-driven approach for addressing multistage stochastic linear optimization problems with unknown distributions. The approach involves solving a robust optimization problem to approximate the underlying stochastic problem and provides asymptotic optimality guarantees. The research shows that this approach can achieve asymptotic optimality in the presence of arbitrarily correlated uncertainty. Finally, numerical experiments demonstrate the practical value of the proposed method in stylized data-driven inventory management problems.