Sampling methods for multistage robust convex optimization problems

TL;DR

This paper introduces a scenario-with-certificates sampling approach for multistage robust convex optimization, reducing sample complexity and providing probabilistic guarantees without relying on decision rules.

Contribution

It presents a novel sampling method that improves efficiency and reliability guarantees in multistage robust convex optimization problems.

Findings

Reduced sample complexity for probabilistic guarantees

Explicit bounds on violation probability

Numerical validation on inventory management problem

Abstract

In this paper, probabilistic guarantees for constraint sampling of multistage robust convex optimization problems are derived. The dynamic nature of these problems is tackled via the so-called scenario-with-certificates approach. This allows to avoid the conservative use of explicit parametrizations through decision rules, and provides a significant reduction of the sample complexity to satisfy a given level of reliability. An explicit bound on the probability of violation is also given. Numerical results dealing with a multistage inventory management problem show the efficacy of the proposed approach.