Code for Convergence and Inference of Stream SGD

This repository contains the code accompanying the paper:

Convergence and Inference of Stream SGD, with Applications to Queueing Systems and Inventory Control

If you find this repository helpful in your research, please consider citing our paper.

Directory Structure

.
├── inventory         # Code for inventory control
├── queue            # Code for queueing system
└── README.md

Each directory contains three subdirectories: convergence, inference, and regret, corresponding to the three tasks analyzed in our paper. These subdirectories contain the relevant Python files for each task.

How to Use the Code

To run an experiment, execute the corresponding main_xxxx_xxx.py file.

For example, to estimate the regret for the queueing system under the M/M/1 setting, run the following command:

cd queue/regret
python main_regret_MM1.py

Notes

Some experimental setups require additional hyperparameters to be adjusted in the Python files. Key details include:

1. Queueing experiments (M/G/1 setup):

   • There is an additional parameter, csv, representing the squared coefficient of variation.
   • The paper considers two values for this parameter: 0.5 and 1.5 (see Appendix for details).

2. Notation:

   • M: Number of repeated experiments.
   • alpha: Controls the decay rate of step sizes.

3. Step size selection in queueing experiments:

   • We use different step sizes for the two parameters, but both decay at the same rate controlled by alpha.
   • Experimentally, using different step sizes improves convergence.
   • The parameters p1 and p2 control the ratio of step sizes. The default choice is (p1, p2) = (1, 5).

4. Inventory control experiments:

   • There is an additional hyperparameter, tau, which represents the lead time in the inventory system.

Acknowledgments

We sincerely thank Guiyu Hong for his assistance in preparing the code for the queueing system experiments.