Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach

• URL: http://arxiv.org/abs/2401.12686v2
• Date: Fri, 23 Feb 2024 10:04:14 GMT
• Title: Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach
• Authors: Christian Fabian, Kai Cui, Heinz Koeppl
• Abstract summary: Mean Field Games (MFGs) can be extended to Graphon MFGs (GMFGs) to include network structures between agents. We introduce the novel concept of Graphex MFGs which builds on the graph theoretical concept of graphexes. This hybrid graphex learning approach leverages that the system mainly consists of a highly connected core and a sparse periphery.
• Score: 31.82185019324094
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Scalable and Accurate Graph Reasoning with LLM-based Multi-Agents [27.4884498301785]
  We introduce GraphAgent-Reasoner, a fine-tuning-free framework for explicit and precise graph reasoning. Inspired by distributed graph computation theory, our framework decomposes graph problems into smaller, node-centric tasks that are distributed among multiple agents. Our framework demonstrates the capability to handle real-world graph reasoning applications such as webpage importance analysis.
  arXiv  Detail & Related papers  (2024-10-07T15:34:14Z)
• MGNet: Learning Correspondences via Multiple Graphs [78.0117352211091]
  Learning correspondences aims to find correct correspondences from the initial correspondence set with an uneven correspondence distribution and a low inlier rate. Recent advances usually use graph neural networks (GNNs) to build a single type of graph or stack local graphs into the global one to complete the task. We propose MGNet to effectively combine multiple complementary graphs.
  arXiv  Detail & Related papers  (2024-01-10T07:58:44Z)
• Graph Transformers for Large Graphs [57.19338459218758]
  This work advances representation learning on single large-scale graphs with a focus on identifying model characteristics and critical design constraints. A key innovation of this work lies in the creation of a fast neighborhood sampling technique coupled with a local attention mechanism. We report a 3x speedup and 16.8% performance gain on ogbn-products and snap-patents, while we also scale LargeGT on ogbn-100M with a 5.9% performance improvement.
  arXiv  Detail & Related papers  (2023-12-18T11:19:23Z)
• GraphGPT: Graph Instruction Tuning for Large Language Models [27.036935149004726]
  Graph Neural Networks (GNNs) have evolved to understand graph structures. To enhance robustness, self-supervised learning (SSL) has become a vital tool for data augmentation. Our research tackles this by advancing graph model generalization in zero-shot learning environments.
  arXiv  Detail & Related papers  (2023-10-19T06:17:46Z)
• SimTeG: A Frustratingly Simple Approach Improves Textual Graph Learning [131.04781590452308]
  We present SimTeG, a frustratingly Simple approach for Textual Graph learning. We first perform supervised parameter-efficient fine-tuning (PEFT) on a pre-trained LM on the downstream task. We then generate node embeddings using the last hidden states of finetuned LM.
  arXiv  Detail & Related papers  (2023-08-03T07:00:04Z)
• Learning Sparse Graphon Mean Field Games [26.405495663998828]
  Graphon mean field games (GMFGs) enable the scalable analysis of MARL problems that are otherwise intractable. Our paper introduces a novel formulation of GMFGs, called LPGMFGs, which leverages the graph theoretical concept of $Lp$ graphons. This especially includes power law networks which are empirically observed in various application areas and cannot be captured by standard graphons.
  arXiv  Detail & Related papers  (2022-09-08T15:35:42Z)
• Federated Graph Machine Learning: A Survey of Concepts, Techniques, and Applications [26.13397777812025]
  Federated Graph Machine Learning (FGML) is a promising solution to tackle this challenge. We conduct a comprehensive review of the literature in FGML. We summarize the real-world applications of FGML from different domains.
  arXiv  Detail & Related papers  (2022-07-24T20:46:23Z)
• GraphMAE: Self-Supervised Masked Graph Autoencoders [52.06140191214428]
  We present a masked graph autoencoder GraphMAE that mitigates issues for generative self-supervised graph learning. We conduct extensive experiments on 21 public datasets for three different graph learning tasks. The results manifest that GraphMAE--a simple graph autoencoder with our careful designs--can consistently generate outperformance over both contrastive and generative state-of-the-art baselines.
  arXiv  Detail & Related papers  (2022-05-22T11:57:08Z)
• What's Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders [32.42097625708298]
  MaskGAE is a self-supervised learning framework for graph-structured data. MGM is a principled pretext task - masking a portion of edges and attempting to reconstruct the missing part with partially visible, unmasked graph structure. We establish close connections between GAEs and contrastive learning, showing that MGM significantly improves the self-supervised learning scheme of GAEs.
  arXiv  Detail & Related papers  (2022-05-20T09:45:57Z)
• Towards Unsupervised Deep Graph Structure Learning [67.58720734177325]
  We propose an unsupervised graph structure learning paradigm, where the learned graph topology is optimized by data itself without any external guidance. Specifically, we generate a learning target from the original data as an "anchor graph", and use a contrastive loss to maximize the agreement between the anchor graph and the learned graph.
  arXiv  Detail & Related papers  (2022-01-17T11:57:29Z)
• Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings [53.58077686470096]
  We propose an end-to-end graph learning framework, namely Iterative Deep Graph Learning (IDGL) for jointly and iteratively learning graph structure and graph embedding. Our experiments show that our proposed IDGL models can consistently outperform or match the state-of-the-art baselines.
  arXiv  Detail & Related papers  (2020-06-21T19:49:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.