Machine learning driven extended matrix norm method for the solution of large-scale zero-sum matrix games

Burhaneddin İzgi*, Murat Özkaya, Nazım Kemal Üre, Matjaž Perc

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Özet

In this paper, we develop a novel machine learning-driven framework for solving large-scale zero-sum matrix games by exploiting patterns discovered from the offline extended matrix norm method. Modern game theoretic tools such as the extended matrix norm method allow rapid estimation of the game values for small-scale zero-sum games by computing norms of the payoff matrix. However, as the number of strategies in the game increases, obtaining an accurate value estimation through the extended matrix norm method becomes more difficult. In this work, we propose a novel neural network architecture for large-scale zero-sum matrix games, which takes the estimations of the extended matrix norm method and payoff matrix as inputs, and provides a rapid estimation of the game value as the output. The proposed architecture is trained over various random zero-sum games of different dimensions. Results show that the developed framework can obtain accurate value predictions, with a less than 10% absolute relative error, for games with up to 50 strategies. Also of note, after the network is trained, solution predictions can be obtained in real-time, which makes the proposed method particularly useful for real-world applications.

Orijinal dilİngilizce
Makale numarası101997
DergiJournal of Computational Science
Hacim68
DOI'lar
Yayın durumuYayınlandı - Nis 2023

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Publisher Copyright:
© 2023 Elsevier B.V.

Finansman

This work is supported by the Scientific and Technological Research Council of Turkey(in Turkish: TÜBİTAK) under grant agreement 121E394 . M.P. is supported by the Slovenian Research Agency (Grant Nos. P1-0403 and J1-2457 ). B.İ. and N.K.Ü. are supported by the Scientific Research Project Unit (BAP) of Istanbul Technical University (project no. MOA-2019-42321 ). The authors would like to thank the anonymous referees and the editor for their valuable suggestions and comments that helped to improve the content of the article.

FinansörlerFinansör numarası
Javna Agencija za Raziskovalno Dejavnost RSP1-0403, J1-2457
Türkiye Bilimsel ve Teknolojik Araştırma Kurumu121E394
Istanbul Teknik ÜniversitesiMOA-2019-42321

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