Learning with Interactive Models over Decision-Dependent Distributions

Man-Jie Yuan, Wei Gao
Proceedings of The 14th Asian Conference on Machine Learning, PMLR 189:1229-1244, 2023.

Abstract

Classical supervised learning generally trains one model from an i.i.d. data according to an unknown yet fixed distribution. In some real applications such as finance, however, multiple models may be trained by different companies and interacted in a dynamic environment, where the data distribution may take shift according to different models’ decisions. In this work, we study two models for simplicity, and formalize such scenario as a learning problem of two models over decision-dependent distributions. We develop the Repeated Risk Minimization (RRM) for two models, and present a sufficient condition to the existence of stable points for RRM, that is, an equilibrium notion. We further provide the theoretical analysis for the convergence of RRM to stable points based on data distribution and finite training sample, respectively. We also study more practical algorithms, such as gradient descent and stochastic gradient descent, to solve the RRM problem with convergence guarantees and we finally present some empirical studies to validate our theoretical analysis.

Cite this Paper

BibTeX
@InProceedings{pmlr-v189-yuan23a, title = {Learning with Interactive Models over Decision-Dependent Distributions}, author = {Yuan, Man-Jie and Gao, Wei}, booktitle = {Proceedings of The 14th Asian Conference on Machine Learning}, pages = {1229--1244}, year = {2023}, editor = {Khan, Emtiyaz and Gonen, Mehmet}, volume = {189}, series = {Proceedings of Machine Learning Research}, month = {12--14 Dec}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v189/yuan23a/yuan23a.pdf}, url = {https://proceedings.mlr.press/v189/yuan23a.html}, abstract = {Classical supervised learning generally trains one model from an i.i.d. data according to an unknown yet fixed distribution. In some real applications such as finance, however, multiple models may be trained by different companies and interacted in a dynamic environment, where the data distribution may take shift according to different models’ decisions. In this work, we study two models for simplicity, and formalize such scenario as a learning problem of two models over decision-dependent distributions. We develop the Repeated Risk Minimization (RRM) for two models, and present a sufficient condition to the existence of stable points for RRM, that is, an equilibrium notion. We further provide the theoretical analysis for the convergence of RRM to stable points based on data distribution and finite training sample, respectively. We also study more practical algorithms, such as gradient descent and stochastic gradient descent, to solve the RRM problem with convergence guarantees and we finally present some empirical studies to validate our theoretical analysis.} }
Endnote
%0 Conference Paper %T Learning with Interactive Models over Decision-Dependent Distributions %A Man-Jie Yuan %A Wei Gao %B Proceedings of The 14th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Emtiyaz Khan %E Mehmet Gonen %F pmlr-v189-yuan23a %I PMLR %P 1229--1244 %U https://proceedings.mlr.press/v189/yuan23a.html %V 189 %X Classical supervised learning generally trains one model from an i.i.d. data according to an unknown yet fixed distribution. In some real applications such as finance, however, multiple models may be trained by different companies and interacted in a dynamic environment, where the data distribution may take shift according to different models’ decisions. In this work, we study two models for simplicity, and formalize such scenario as a learning problem of two models over decision-dependent distributions. We develop the Repeated Risk Minimization (RRM) for two models, and present a sufficient condition to the existence of stable points for RRM, that is, an equilibrium notion. We further provide the theoretical analysis for the convergence of RRM to stable points based on data distribution and finite training sample, respectively. We also study more practical algorithms, such as gradient descent and stochastic gradient descent, to solve the RRM problem with convergence guarantees and we finally present some empirical studies to validate our theoretical analysis.
APA
Yuan, M. & Gao, W.. (2023). Learning with Interactive Models over Decision-Dependent Distributions. Proceedings of The 14th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 189:1229-1244 Available from https://proceedings.mlr.press/v189/yuan23a.html.

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