This is supporting code for "Model-sharing Games: Analyzing Federated Learning Under Voluntary Participation" (https://arxiv.org/abs/2010.00753, AAAI 2021) and "Optimality and Stability in Federated Learning: A Game-theoretic Approach" (https://arxiv.org/abs/2106.09580, NeurIPS 2021). Note that all of the results in these papers are theoretical and so none of them strictly depend on the results in these notebooks. However, we did end up writing code during the process these papers, mainly to check conjectures and verifying that theorems matched our intuition. Hopefully, these notebooks will be useful for readers who wish to experiment with our area of study themselves. If you have any questions or find any errors, please email kdonahue@cs.cornell.edu.
The first three notebooks primarily relate to "Model-Sharing Games", while the fourth primarily relates to "Optimality and Stability in Federated Learning".
01_mean_simulation calculates exact MSE for the mean estimation case and performs simulations for the same case, to verify that they are the same, up to noise.
02_regression_simulation does the same analysis for the linear regression case. In the limit where n>>D (there are many more data points than the dimension of the linear regression problem), linear regression has the same error as mean estimation, so future cases simply use the mean estimation errors.
03_calculate_stability uses the results of 01_mean_simulation to build tools for determining which arrangements of a given set of players are stable. It also reproduces tables and error values used in the Motivating Example section and the core stability exploration in the end of Appendix D.
04_calculate_stability_optimality is an adapted version of 03_calculate_stability that considers both stability and optimality (minimizing some notion of cost).
Python: 3.7.5
numpy: 1.17.1
pandas: 0.25.3
scipy: 1.3.1
matplotlib: 3.1.1
more-itertools: 7.2.0