Learning in Stochastic Monotone Games with Decision-Dependent Data
Adhyyan Narang, Evan Faulkner, Dmitriy Drusvyatskiy, Maryam Fazel, Lillian Ratliff
Abstract
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers’ actions. This paper formulates a new game theoretic framework for this phenomenon, called multi-player performative prediction. We establish transparent sufficient conditions for strong monotonicity of the game and use them to develop algorithms for finding Nash equilibria. We investigate derivative free methods and adaptive gradient algorithms wherein each player alternates between learning a parametric description of their distribution and gradient steps on the empirical risk. Synthetic and semi-synthetic numerical experiments illustrate the results.
BibTeX
@InProceedings{pmlr-v151-narang22a,
title = { Learning in Stochastic Monotone Games with Decision-Dependent Data },
author = {Narang, Adhyyan and Faulkner, Evan and Drusvyatskiy, Dmitriy and Fazel, Maryam and Ratliff, Lillian},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {5891--5912},
year = {2022},
editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
volume = {151},
series = {Proceedings of Machine Learning Research},
month = {28--30 Mar},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v151/narang22a/narang22a.pdf},
url = {https://proceedings.mlr.press/v151/narang22a.html},
abstract = { Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers’ actions. This paper formulates a new game theoretic framework for this phenomenon, called multi-player performative prediction. We establish transparent sufficient conditions for strong monotonicity of the game and use them to develop algorithms for finding Nash equilibria. We investigate derivative free methods and adaptive gradient algorithms wherein each player alternates between learning a parametric description of their distribution and gradient steps on the empirical risk. Synthetic and semi-synthetic numerical experiments illustrate the results. }
}