Fabian, Christian ; Cui, Kai ; Koeppl, Heinz (2024)
Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach.
International Conference on Learning Representations. Vienna, Austria (07.05.2024 - 11.05.2024)
doi: 10.26083/tuprints-00028691
Konferenzveröffentlichung, Zweitveröffentlichung, Postprint
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Kurzbeschreibung (Abstract)
Learning the behavior of large agent populations is an important task for numerous research areas. Although the field of multi-agent reinforcement learning (MARL) has made significant progress towards solving these systems, solutions for many agents often remain computationally infeasible and lack theoretical guarantees. Mean Field Games (MFGs) address both of these issues and can be extended to Graphon MFGs (GMFGs) to include network structures between agents. Despite their merits, the real world applicability of GMFGs is limited by the fact that graphons only capture dense graphs. Since most empirically observed networks show some degree of sparsity, such as power law graphs, the GMFG framework is insufficient for capturing these network topologies. Thus, we introduce the novel concept of Graphex MFGs (GXMFGs) which builds on the graph theoretical concept of graphexes. Graphexes are the limiting objects to sparse graph sequences that also have other desirable features such as the small world property. Learning equilibria in these games is challenging due to the rich and sparse structure of the underlying graphs. To tackle these challenges, we design a new learning algorithm tailored to the GXMFG setup. This hybrid graphex learning approach leverages that the system mainly consists of a highly connected core and a sparse periphery. After defining the system and providing a theoretical analysis, we state our learning approach and demonstrate its learning capabilities on both synthetic graphs and real-world networks. This comparison shows that our GXMFG learning algorithm successfully extends MFGs to a highly relevant class of hard, realistic learning problems that are not accurately addressed by current MARL and MFG methods.
| Typ des Eintrags: | Konferenzveröffentlichung |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Fabian, Christian ; Cui, Kai ; Koeppl, Heinz |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach |
| Sprache: | Englisch |
| Publikationsjahr: | 25 November 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | 9 Mai 2024 |
| Verlag: | ICLR |
| Buchtitel: | ICLR 2024 The Twelfth International Conference on Learning Representations |
| Kollation: | 39 Seiten |
| Veranstaltungstitel: | International Conference on Learning Representations |
| Veranstaltungsort: | Vienna, Austria |
| Veranstaltungsdatum: | 07.05.2024 - 11.05.2024 |
| DOI: | 10.26083/tuprints-00028691 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/28691 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichungsservice |
| Kurzbeschreibung (Abstract): | Learning the behavior of large agent populations is an important task for numerous research areas. Although the field of multi-agent reinforcement learning (MARL) has made significant progress towards solving these systems, solutions for many agents often remain computationally infeasible and lack theoretical guarantees. Mean Field Games (MFGs) address both of these issues and can be extended to Graphon MFGs (GMFGs) to include network structures between agents. Despite their merits, the real world applicability of GMFGs is limited by the fact that graphons only capture dense graphs. Since most empirically observed networks show some degree of sparsity, such as power law graphs, the GMFG framework is insufficient for capturing these network topologies. Thus, we introduce the novel concept of Graphex MFGs (GXMFGs) which builds on the graph theoretical concept of graphexes. Graphexes are the limiting objects to sparse graph sequences that also have other desirable features such as the small world property. Learning equilibria in these games is challenging due to the rich and sparse structure of the underlying graphs. To tackle these challenges, we design a new learning algorithm tailored to the GXMFG setup. This hybrid graphex learning approach leverages that the system mainly consists of a highly connected core and a sparse periphery. After defining the system and providing a theoretical analysis, we state our learning approach and demonstrate its learning capabilities on both synthetic graphs and real-world networks. This comparison shows that our GXMFG learning algorithm successfully extends MFGs to a highly relevant class of hard, realistic learning problems that are not accurately addressed by current MARL and MFG methods. |
| Status: | Postprint |
| URN: | urn:nbn:de:tuda-tuprints-286912 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 000 Allgemeines, Informatik, Informationswissenschaft > 004 Informatik 600 Technik, Medizin, angewandte Wissenschaften > 621.3 Elektrotechnik, Elektronik |
| Fachbereich(e)/-gebiet(e): | 18 Fachbereich Elektrotechnik und Informationstechnik 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Nachrichtentechnik > Bioinspirierte Kommunikationssysteme 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Nachrichtentechnik 18 Fachbereich Elektrotechnik und Informationstechnik > Self-Organizing Systems Lab |
| Hinterlegungsdatum: | 25 Nov 2024 10:43 |
| Letzte Änderung: | 28 Nov 2024 08:53 |
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| Suche nach Titel in: | TUfind oder in Google |
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- Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach. (deposited 25 Nov 2024 10:43) [Gegenwärtig angezeigt]
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