{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-sparse-graphon-mean-field-games","title":"Learning Sparse Graphon Mean Field Games","arxiv_id":"2209.03880","date":"2022-09-08","proceeding":null,"authors":["Christian Fabian","Kai Cui","Heinz Koeppl"],"abstract":"Although the field of multi-agent reinforcement learning (MARL) has made considerable progress in the last years, solving systems with a large number of agents remains a hard challenge. Graphon mean field games (GMFGs) enable the scalable analysis of MARL problems that are otherwise intractable. By the mathematical structure of graphons, this approach is limited to dense graphs which are insufficient to describe many real-world networks such as power law graphs. Our paper introduces a novel formulation of GMFGs, called LPGMFGs, which leverages the graph theoretical concept of $L^p$ graphons and provides a machine learning tool to efficiently and accurately approximate solutions for sparse network problems. This especially includes power law networks which are empirically observed in various application areas and cannot be captured by standard graphons. We derive theoretical existence and convergence guarantees and give empirical examples that demonstrate the accuracy of our learning approach for systems with many agents. Furthermore, we extend the Online Mirror Descent (OMD) learning algorithm to our setup to accelerate learning speed, empirically show its capabilities, and conduct a theoretical analysis using the novel concept of smoothed step graphons. In general, we provide a scalable, mathematically well-founded machine learning approach to a large class of otherwise intractable problems of great relevance in numerous research fields.","url_abs":"https://arxiv.org/abs/2209.03880v3","url_pdf":"https://arxiv.org/pdf/2209.03880v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-sparse-graphon-mean-field-games","repo_url":"https://github.com/chrfabian/learning_sparse_gmfgs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"multi-agent-reinforcement-learning","task_name":"Multi-agent Reinforcement Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2209.03880","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2209.03880"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/chrfabian/learning_sparse_gmfgs","reach":null}],"summary":{"ran_draft_wrong":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"817ce1100c2e7c79","entry":"run_once","repo":"chrfabian/learning_sparse_gmfgs","repo_kind":"official","path":"experiments/run_once_nagent_compare_sparse.py","file_url":"https://github.com/chrfabian/learning_sparse_gmfgs/blob/HEAD/experiments/run_once_nagent_compare_sparse.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"817ce1100c2e7c79"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}