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|a 10.1109/TPAMI.2024.3445666
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|a eng
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|a Chen, Guanpu
|e verfasserin
|4 aut
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|a Approaching the Global Nash Equilibrium of Non-Convex Multi-Player Games
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|c 2024
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|a Text
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|a Date Revised 08.11.2024
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|a published: Print-Electronic
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|a Citation Status PubMed-not-MEDLINE
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|a Many machine learning problems can be formulated as non-convex multi-player games. Due to non-convexity, it is challenging to obtain the existence condition of the global Nash equilibrium (NE) and design theoretically guaranteed algorithms. This paper studies a class of non-convex multi-player games, where players' payoff functions consist of canonical functions and quadratic operators. We leverage conjugate properties to transform the complementary problem into a variational inequality (VI) problem using a continuous pseudo-gradient mapping. We prove the existence condition of the global NE as the solution to the VI problem satisfies a duality relation. We then design an ordinary differential equation to approach the global NE with an exponential convergence rate. For practical implementation, we derive a discretized algorithm and apply it to two scenarios: multi-player games with generalized monotonicity and multi-player potential games. In the two settings, step sizes are required to be O(1/k) and O(1/√k) to yield the convergence rates of O(1/ k) and O(1/√k), respectively. Extensive experiments on robust neural network training and sensor network localization validate our theory. Our code is available at https://github.com/GuanpuChen/Global-NE
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|a Journal Article
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|a Xu, Gehui
|e verfasserin
|4 aut
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| 700 |
1 |
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|a He, Fengxiang
|e verfasserin
|4 aut
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| 700 |
1 |
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|a Hong, Yiguang
|e verfasserin
|4 aut
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| 700 |
1 |
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|a Rutkowski, Leszek
|e verfasserin
|4 aut
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| 700 |
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|a Tao, Dacheng
|e verfasserin
|4 aut
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| 773 |
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|i Enthalten in
|t IEEE transactions on pattern analysis and machine intelligence
|d 1979
|g 46(2024), 12 vom: 15. Nov., Seite 10797-10813
|w (DE-627)NLM098212257
|x 1939-3539
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|g volume:46
|g year:2024
|g number:12
|g day:15
|g month:11
|g pages:10797-10813
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|u http://dx.doi.org/10.1109/TPAMI.2024.3445666
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