Learning Mean Field Control on Sparse Graphs
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915633737760768 |
|---|---|
| author | Fabian, Christian Cui, Kai Koeppl, Heinz |
| author_facet | Fabian, Christian Cui, Kai Koeppl, Heinz |
| contents | Large agent networks are abundant in applications and nature and pose difficult challenges in the field of multi-agent reinforcement learning (MARL) due to their computational and theoretical complexity. While graphon mean field games and their extensions provide efficient learning algorithms for dense and moderately sparse agent networks, the case of realistic sparser graphs remains largely unsolved. Thus, we propose a novel mean field control model inspired by local weak convergence to include sparse graphs such as power law networks with coefficients above two. Besides a theoretical analysis, we design scalable learning algorithms which apply to the challenging class of graph sequences with finite first moment. We compare our model and algorithms for various examples on synthetic and real world networks with mean field algorithms based on Lp graphons and graphexes. As it turns out, our approach outperforms existing methods in many examples and on various networks due to the special design aiming at an important, but so far hard to solve class of MARL problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Mean Field Control on Sparse Graphs Fabian, Christian Cui, Kai Koeppl, Heinz Multiagent Systems Artificial Intelligence Computer Science and Game Theory Machine Learning Large agent networks are abundant in applications and nature and pose difficult challenges in the field of multi-agent reinforcement learning (MARL) due to their computational and theoretical complexity. While graphon mean field games and their extensions provide efficient learning algorithms for dense and moderately sparse agent networks, the case of realistic sparser graphs remains largely unsolved. Thus, we propose a novel mean field control model inspired by local weak convergence to include sparse graphs such as power law networks with coefficients above two. Besides a theoretical analysis, we design scalable learning algorithms which apply to the challenging class of graph sequences with finite first moment. We compare our model and algorithms for various examples on synthetic and real world networks with mean field algorithms based on Lp graphons and graphexes. As it turns out, our approach outperforms existing methods in many examples and on various networks due to the special design aiming at an important, but so far hard to solve class of MARL problems. |
| title | Learning Mean Field Control on Sparse Graphs |
| topic | Multiagent Systems Artificial Intelligence Computer Science and Game Theory Machine Learning |
| url | https://arxiv.org/abs/2501.17079 |