A kernel based stochastic approximation framework for contextual optimization

This archive is distributed under the MIT License.

The software and data in this repository are a snapshot of the software that was used in the research reported on in the paper A kernel-based stochastic approximation framework for contextual optimization by Hao Cao, Jian-Qiang Hu, and Jiaqiao Hu.

Cite

To cite the contents of this repository, please cite the paper.

@misc{cao2024kernel,
  author =        {Hao Cao and Jian-Qiang Hu and Jiaqiao Hu},
  journal =       {SSRN Electronic Journal},
  title =         {A kernel based stochastic approximation framework for contextual optimization},
  year =          {2024},
  note =          {Available at SSRN: https://ssrn.com/abstract=5411562},
  url  =          {https://ssrn.com/abstract=5411562},
}  

Description

The goal of this software is to demonstrate a kernel-based stochastic approximation (KBSA) framework for solving contextual stochastic optimization problems with differentiable objective functions, including conditional expectations, conditional quantiles, and many co-risk measures such as CoVaR and CoES. This unifying algorithmic framework can not only be applied for estimating multiple contextual measures but also allows their sensitivity analysis and optimization.

Structure

The structure of this repository is as follows:

• src/KBSA.py: The code of the proposed kernel-based stochastic approximation (KBSA) algorithm.
• scripts/: The directory containing implementation examples.
• results/: The directory storing the figures included in the paper.

Requirements

The code is tested in the environment of Python 3.12.4 with Windows 11.

Numerous package requirements exist, including but not limited to: numpy, pandas, matplotlib, scipy, operator, IPython, random, itertools, math, pickle, joblib, seaborn, and statsmodels. For configuration details, please refer to the conda environment manifest file scripts/environment.yml.

Results

We provide detailed implementation guidances and demonstrate results in the scripts/ directory. It suffices just to run each notebook (you can execute cells individually). We have generated all the data used in the paper——no external data sources are required.

• KBSA_test_mean.ipynb: The Python notebook containing implementation guidances for reproducing the results in the blackbox test functions examples with Cost 1;
• KBSA_test_risk.ipynb: The Python notebook containing implementation guidances for reproducing the results in the blackbox test functions examples with Cost 2;
• KBSA_portfolio.ipynb: The Python notebook containing implementation guidances for reproducing the results in the nonlinear portfolios example.