On the computational complexity and generalization properties of multi-stage and recursive scenario programs

TL;DR

This paper analyzes the computational complexity and feasibility of various scenario-based methods for uncertain optimization, highlighting trade-offs and benefits of recursive algorithms in decision-making.

Contribution

It compares standard and recursive scenario approaches, revealing their complexity and feasibility trade-offs based on problem structure and constraint satisfaction goals.

Findings

Recursive algorithms can reduce complexity in uncertain optimization.

Trade-offs exist between feasibility and computational burden.

Recursive methods are effective in approximate dynamic programming.

Abstract

We discuss the computational complexity and feasibility properties of scenario based techniques for uncertain optimization programs. We consider different solution alternatives ranging from the standard scenario approach to recursive variants, and compare feasibility as a function of the total computation burden. We identify trade-offs between the different methods depending on the problem structure and the desired probability of constraint satisfaction. Our motivation for this work stems from the applicability and complexity reduction when making decisions by means of recursive algorithms. We illustrate our results on an example from the area of approximate dynamic programming