A Note on Piecewise Affine Decision Rules for Robust, Stochastic, and Data-Driven Optimization

TL;DR

This paper introduces an improved algorithmic framework for multi-stage decision-making under uncertainty, enhancing policy quality and extending applicability to robust and data-driven optimization.

Contribution

It revisits and improves a popular approximation scheme for stochastic programs, making it more efficient and versatile for various optimization settings.

Findings

The framework delivers superior policies in stochastic settings.

It extends applicability to robust and Wasserstein-based data-driven optimization.

Numerical experiments demonstrate the benefits of the proposed method.

Abstract

Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges involved, these problems are typically solved approximately. This short note introduces an algorithmic framework that revisits a popular approximation scheme for multi-stage stochastic programs by Georghiou et al. (2015) and improves upon it to deliver superior policies in the stochastic setting, as well as extend its applicability to robust optimization and a contemporary Wasserstein-based data-driven setting. We demonstrate how the policies of our framework can be computed efficiently, and we present numerical experiments that highlight the benefits of our method.