This repository contains all files necessary to reproduce the results in the paper Minimax Optimal Estimation of Stability Under Distribution Shift, the arXiv version is available at this link.

File Structure

• Simulation Stability.ipynb
  _{All the code to generate results for the simulation setting: Figures 2 and 3.}

• Stability_Statistical_Model_NHIS.ipynb
  _{All the code to generate results for the Health utilization prediction model (NHIS) in Section 5.2 and the appendix.}

• stability_queue_code/
  _{All the code to generate results for queueing systems in Section 5.1 and the appendix.}

  • model_train_3920_2022-01-28_04/01/39.pkl #the DQN model trained using the file train_DQN.py, which is also the DQN model in the paper
  • Stability_queue_convergence.py # generate data for Figure 5
  • Stability_queue_functions.py # all functions necessary for queueing systems
  • Stability_queue_kde.py # generate data for Figure 5 (the KDE estimator)
  • Stability_queue.ipynb # code to generate plots for queueing systems
  • train_DQN.py # the script to train the DQN model model_train_3920_2022-01-28_04/01/39.pkl

Data

• Simulation

  Data is generated in the notebook.

• NHIS

  Data is available upon request.

• Queueing models

  To run the queueing systems code for Figure 4 and Figures 7 - 11, one needs to generate data using the scripts given in Stability_queue.ipynb. For example, in the below code block, the first line of code generates data and saved it to a file, the second line read the saved data and perform plotting Note that each file will contain a time of generation for versioning purposes: one should modify the time appropriately when reading the file. In the below example, one should change _2023-08-14_12:59:34 appropriately.

  evaluate_policy_under_distribution(arrival_distribution_t1, service_distribution_t1, mixture_prob_arrival, mixture_prob_service,'distribution_shift_type_1_new',number_of_simulations = 10000)
  data_0 = joblib.load('./Result/model_data/distribution_shift_type_1_10K_data__2023-08-14_12:59:34.pkl')
  evaluate_policy_under_distribution(arrival_distribution_t1, service_distribution_t1, mixture_prob_arrival, mixture_prob_service,'distribution_shift_type_1_new',1,data_0)

Creating the Environment

To replicate the environment for all code, you can install the required packages using the command below. Note that not all packages are necessary. As most packages used in this project are standard, we recommend manually installing any missing packages if issues arise when running the below command.

conda create -n stability_env python=3.10.12
conda activate stability_env
pip install -r requirements.txt

Additional instructions

• All file paths in the code needs to be changed appropriately, for example, file_path = '/user/ym2865/NHIS/model_file/' in the code needs to be changed to your directory
• For each code in all notebooks, there is a description on what this code corresponds to (e.g., generate data for Figure 1, or generate Figure 1).

Authors

• Hongseok Namkoong, Yuanzhe Ma, and Peter W. Glynn
• For any questions, please contact Yuanzhe Ma at ym2865@columbia.edu.

Citation

@article{NamkoongMaGlynn25,
author = {Namkoong, Hongseok and Ma, Yuanzhe and Glynn, Peter W.},
title = {Minimax Optimal Estimation of Stability Under Distribution Shift},
journal = {Operations Research}, 
year = {2025},
doi = {10.1287/opre.2022.0658}
}