Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions

Asish Ghoshal, Jean Honorio
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:1532-1540, 2017.

Abstract

In this paper we obtain sufficient and necessary conditions on the number of samples required for exact recovery of the pure-strategy Nash equilibria (PSNE) set of a graphical game from noisy observations of joint actions. We consider sparse linear influence games — a parametric class of graphical games with linear payoffs, and represented by directed graphs of n nodes (players) and in-degree of at most k. We show that one can efficiently recover the PSNE set of a linear influence game with $O(k^2 \log n)$ samples, under very general observation models. On the other hand, we show that $Ω(k \log n)$ samples are necessary for any procedure to recover the PSNE set from observations of joint actions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-ghoshal17b, title = {{Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions}}, author = {Ghoshal, Asish and Honorio, Jean}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {1532--1540}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/ghoshal17b/ghoshal17b.pdf}, url = {https://proceedings.mlr.press/v54/ghoshal17b.html}, abstract = {In this paper we obtain sufficient and necessary conditions on the number of samples required for exact recovery of the pure-strategy Nash equilibria (PSNE) set of a graphical game from noisy observations of joint actions. We consider sparse linear influence games — a parametric class of graphical games with linear payoffs, and represented by directed graphs of n nodes (players) and in-degree of at most k. We show that one can efficiently recover the PSNE set of a linear influence game with $O(k^2 \log n)$ samples, under very general observation models. On the other hand, we show that $Ω(k \log n)$ samples are necessary for any procedure to recover the PSNE set from observations of joint actions.} }
Endnote
%0 Conference Paper %T Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions %A Asish Ghoshal %A Jean Honorio %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-ghoshal17b %I PMLR %P 1532--1540 %U https://proceedings.mlr.press/v54/ghoshal17b.html %V 54 %X In this paper we obtain sufficient and necessary conditions on the number of samples required for exact recovery of the pure-strategy Nash equilibria (PSNE) set of a graphical game from noisy observations of joint actions. We consider sparse linear influence games — a parametric class of graphical games with linear payoffs, and represented by directed graphs of n nodes (players) and in-degree of at most k. We show that one can efficiently recover the PSNE set of a linear influence game with $O(k^2 \log n)$ samples, under very general observation models. On the other hand, we show that $Ω(k \log n)$ samples are necessary for any procedure to recover the PSNE set from observations of joint actions.
APA
Ghoshal, A. & Honorio, J.. (2017). Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:1532-1540 Available from https://proceedings.mlr.press/v54/ghoshal17b.html.

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