Approaching the Global Nash Equilibrium of Non-Convex Multi-Player Games
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...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 46(2024), 12 vom: 15. Nov., Seite 10797-10813 |
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| 1. Verfasser: | |
| Weitere Verfasser: | , , , , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2024
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article |
| Zusammenfassung: | 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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| Beschreibung: | Date Revised 08.11.2024 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2024.3445666 |