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

ArXiv ID: 2310.07052 “View on arXiv”

Authors: Unknown

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.

Keywords: Stochastic Optimization, Portfolio Optimization, Parameter Uncertainty, Sub-sampling, Large-scale Optimization, Multi-Asset (Portfolio)

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper uses advanced stochastic programming, asymptotic convergence theorems, and dense mathematical proofs for optimization under uncertainty, indicating high math complexity. It includes a numerical portfolio optimization study with sub-sample estimates, demonstrating data-heavy implementation and backtest-ready concepts for reducing estimation errors.

  flowchart TD
    A["Research Goal: Improve Large-Scale Stochastic Optimization<br>by Reducing Errors from Parameter Uncertainty"] --> B["Methodology: Optimization using Sub-sample<br>Estimates vs. Full-sample Estimates"]
    B --> C["Data Input: Multi-Asset Portfolio Data<br>with Parameter Uncertainty"]
    C --> D["Computational Process: Solving Stochastic<br>Optimization Models"]
    D --> E{"Comparison of<br>Solutions"}
    E --> F["Outcome 1: Sub-sample Optimization<br>Reduces Errors & Improves Robustness"]
    E --> G["Outcome 2: Identifies Problem Structures<br>Benefiting Most from Sub-sampling"]
    F --> H["Theoretical Analysis: Validates<br>Asymptotic Convergence Limits"]
    G --> H