Uses of Sub-sample Estimates to Reduce Errors in Stochastic Optimization Models

TL;DR

This paper explores how using sub-sample estimates in large-scale stochastic optimization can reduce errors and improve solutions, especially when full-sample methods are misled by sample variability.

Contribution

It introduces a theoretical framework and empirical evidence showing the advantages of sub-sample estimates over full-sample solutions in large-scale stochastic optimization.

Findings

Sub-sample estimates can outperform full-sample solutions in large problems.

Numerical results demonstrate improved portfolio optimization outcomes.

Theoretical analysis explains when sub-sampling is most effective.

Abstract

Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or with some form of sample. With large numbers of such parameters, optimization of the resulting model is often driven by mis-specifications or extreme sample characteristics, resulting in solutions that are far from a true optimum. This paper describes how asymptotic convergence results may not be useful in large-scale problems and how the optimization of problems based on sub-sample estimates may achieve improved results over models using full-sample solution estimates. A motivating example and numerical results from a portfolio optimization problem demonstrate the potential improvement. A theoretical analysis also provides insight into the structure of problems where sub-sample optimization may be most beneficial.