Network Effects in Performative Prediction Games

Xiaolu Wang, Chung-Yiu Yau, Hoi To Wai
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:36514-36540, 2023.

Abstract

This paper studies the multi-agent performative prediction (Multi-PP) games over multiplex networks. We consider a distributed learning setting where agents partially cooperate on an agent network, while during learning, the data samples drawn depend on the prediction models of the agent itself and neighboring agents on a population network. The dynamics of Multi-PP games is hence affected by the interplay between both networks. This paper concentrates on this Multi-PP game with the following contributions. Firstly, we analyze sufficient conditions for the existence of the performative stable equilibrium (PSE) and Nash equilibrium (NE) of the Multi-PP games. Secondly, we analyze the changes to the equilibrium induced by perturbed data distributions, and derive the closed-form solutions where the network topologies are explicit. Our results connect the existence of PSE/NE with strengths of agents’ cooperation, and the changes of equilibrium solutions across agents with their node centrality, etc. Lastly, we show that a stochastic gradient descent (SGD) based distributed learning procedure finds the PSE under the said sufficient condition. Numerical illustrations on the network effects in Multi-PP games corroborate our findings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-wang23ap, title = {Network Effects in Performative Prediction Games}, author = {Wang, Xiaolu and Yau, Chung-Yiu and Wai, Hoi To}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {36514--36540}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/wang23ap/wang23ap.pdf}, url = {https://proceedings.mlr.press/v202/wang23ap.html}, abstract = {This paper studies the multi-agent performative prediction (Multi-PP) games over multiplex networks. We consider a distributed learning setting where agents partially cooperate on an agent network, while during learning, the data samples drawn depend on the prediction models of the agent itself and neighboring agents on a population network. The dynamics of Multi-PP games is hence affected by the interplay between both networks. This paper concentrates on this Multi-PP game with the following contributions. Firstly, we analyze sufficient conditions for the existence of the performative stable equilibrium (PSE) and Nash equilibrium (NE) of the Multi-PP games. Secondly, we analyze the changes to the equilibrium induced by perturbed data distributions, and derive the closed-form solutions where the network topologies are explicit. Our results connect the existence of PSE/NE with strengths of agents’ cooperation, and the changes of equilibrium solutions across agents with their node centrality, etc. Lastly, we show that a stochastic gradient descent (SGD) based distributed learning procedure finds the PSE under the said sufficient condition. Numerical illustrations on the network effects in Multi-PP games corroborate our findings.} }
Endnote
%0 Conference Paper %T Network Effects in Performative Prediction Games %A Xiaolu Wang %A Chung-Yiu Yau %A Hoi To Wai %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-wang23ap %I PMLR %P 36514--36540 %U https://proceedings.mlr.press/v202/wang23ap.html %V 202 %X This paper studies the multi-agent performative prediction (Multi-PP) games over multiplex networks. We consider a distributed learning setting where agents partially cooperate on an agent network, while during learning, the data samples drawn depend on the prediction models of the agent itself and neighboring agents on a population network. The dynamics of Multi-PP games is hence affected by the interplay between both networks. This paper concentrates on this Multi-PP game with the following contributions. Firstly, we analyze sufficient conditions for the existence of the performative stable equilibrium (PSE) and Nash equilibrium (NE) of the Multi-PP games. Secondly, we analyze the changes to the equilibrium induced by perturbed data distributions, and derive the closed-form solutions where the network topologies are explicit. Our results connect the existence of PSE/NE with strengths of agents’ cooperation, and the changes of equilibrium solutions across agents with their node centrality, etc. Lastly, we show that a stochastic gradient descent (SGD) based distributed learning procedure finds the PSE under the said sufficient condition. Numerical illustrations on the network effects in Multi-PP games corroborate our findings.
APA
Wang, X., Yau, C. & Wai, H.T.. (2023). Network Effects in Performative Prediction Games. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:36514-36540 Available from https://proceedings.mlr.press/v202/wang23ap.html.

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