mlsanityData to 14 Oct 2026

Mean-Field Control on Sparse Graphs: From Local Limits to GNNs via Neighborhood Distributions

arXiv 2601.21477 ↗First posted 29 Jan 2026cs.MA cs.AI cs.LGcited by 0

On the map: Deep reinforcement learning methods → RL for games and combinatorial optimization

Abstract (arXiv)

Mean-field control (MFC) offers a scalable solution to the curse of dimensionality in multi-agent systems but traditionally hinges on the restrictive assumption of exchangeability via dense, all-to-all interactions. In this work, we bridge the gap to real-world network structures by proposing a rigorous framework for MFC on large sparse graphs. We redefine the system state as a probability measure over decorated rooted neighborhoods, effectively capturing local heterogeneity. Our central contribution is a theoretical foundation for scalable reinforcement learning in this setting. We prove horizon-dependent locality: for finite-horizon problems, an agent's optimal policy at time t depends strictly on its (T-t)-hop neighborhood. This result renders the infinite-dimensional control problem tractable and underpins a novel Dynamic Programming Principle (DPP) on the lifted space of neighborhood distributions. Furthermore, we formally and experimentally justify the use of Graph Neural Networks (GNNs) for actor-critic algorithms in this context. Our framework naturally recovers classical MFC as a degenerate case while enabling efficient, theoretically grounded control on complex sparse topologies.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods. Builds on 25 of its 45 references that are in the map. First posted on arXiv 29 Jan 2026.

Builds on

25 of 45 references.

Closest ancestors · 1

Same direction, newest first

  1. 2025Learning Mean Field Control on Sparse Graphs28 Jan

Other references · 24

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2018How Powerful are Graph Neural Networks?cited by 4,393
  3. 2017Deep Setscited by 1,421
  4. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  5. 2020Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learningcited by 485
  6. 2019Provably Powerful Graph Networkscited by 389
  7. 2018Mean Field Multi-Agent Reinforcement Learningcited by 207
  8. 2018Graph Convolutional Reinforcement Learningcited by 152
  9. 2020Fictitious Play for Mean Field Games: Continuous Time Analysis and Applicationscited by 62
  10. 2022Learning in Mean Field Games: A Surveycited by 61
  11. 2020Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysiscited by 49
  12. 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 38
12 more
  1. 2016Markov-Nash Equilibria in Mean-Field Games with Discounted Costcited by 31
  2. 2021Mean-Field Multi-Agent Reinforcement Learning: A Decentralized Network Approachcited by 28
  3. 2021Generalization in Mean Field Games by Learning Master Policiescited by 28
  4. 2021Learning Graphon Mean Field Games and Approximate Nash Equilibriacited by 28
  5. 2019Dynamic Programming Principles for Mean-Field Controls with Learningcited by 23
  6. 2022Learning Sparse Graphon Mean Field Gamescited by 14
  7. 2020Graphon Mean Field Games and the GMFG Equationscited by 13
  8. 2022Graphon Mean-Field Control for Cooperative Multi-Agent Reinforcement Learningcited by 11
  9. 2023Learning Regularized Monotone Graphon Mean-Field Gamescited by 9
  10. 2023Learning Decentralized Partially Observable Mean Field Control for Artificial Collective Behaviorcited by 7
  11. 2023Learning Regularized Graphon Mean-Field Games with Unknown Graphonscited by 4
  12. 2024Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approachcited by 3

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  1. 2026Sparsity Is Necessary: Polynomial-Time Stability for Agentic LLMs in Large Action Spaces
  2. 2025Sparse shepherding control of large-scale multi-agent systems via Reinforcement Learning
  3. 2025Convergence of Actor-Critic Learning for Mean Field Games and Mean Field Control in Continuous Spaces
  4. 2026Graph-SND: Sparse Aggregation for Behavioral Diversity in Multi-Agent Reinforcement Learning
  5. 2025Distributed Control of Network Systems in the Space of Stabilizing Graph Neural Network Policies
  6. 2024Efficient and Scalable Deep Reinforcement Learning for Mean Field Control Games
  7. 2026Actor-Critic Learning for Extended Mean Field Control with Deterministic Policies
  8. 2025Bayesian Ego-graph Inference for Networked Multi-Agent Reinforcement Learning