{"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/double-matching-under-complementary","title":"Two-sided Competing Matching Recommendation Markets With Quota and Complementary Preferences Constraints","arxiv_id":"2301.10230","date":"2023-01-24","proceeding":null,"authors":["Yuantong Li","Guang Cheng","Xiaowu Dai"],"abstract":"In this paper, we propose a new recommendation algorithm for addressing the problem of two-sided online matching markets with complementary preferences and quota constraints, where agents' preferences are unknown a priori and must be learned from data. The presence of mixed quota and complementary preferences constraints can lead to instability in the matching process, making this problem challenging to solve. To overcome this challenge, we formulate the problem as a bandit learning framework and propose the Multi-agent Multi-type Thompson Sampling (MMTS) algorithm. The algorithm combines the strengths of Thompson Sampling for exploration with a new double matching technique to provide a stable matching outcome. Our theoretical analysis demonstrates the effectiveness of MMTS as it can achieve stability and has a total $\\widetilde{\\mathcal{O}}(Q{\\sqrt{K_{\\max}T}})$-Bayesian regret with high probability, which exhibits linearity with respect to the total firm's quota $Q$, the square root of the maximum size of available type workers $\\sqrt{K_{\\max}}$ and time horizon $T$. In addition, simulation studies also demonstrate MMTS's effectiveness in various settings. We provide code used in our experiments \\url{https://github.com/Likelyt/Double-Matching}.","url_abs":"https://arxiv.org/abs/2301.10230v3","url_pdf":"https://arxiv.org/pdf/2301.10230v3.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":"double-matching-under-complementary","repo_url":"https://github.com/likelyt/double-matching","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"thompson-sampling","task_name":"Thompson Sampling"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2301.10230","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2301.10230"}},"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/likelyt/double-matching","reach":null}],"summary":{"unverified":3},"by_repo_kind":{"official":{"samples":3,"ran":0,"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":3,"samples":[{"code_sha256_prefix":"52aa97f6d9204e6c","entry":"Multi_Agent_DA_with_Type","repo":"likelyt/double-matching","repo_kind":"official","path":"code/MultiAgent.py","file_url":"https://github.com/likelyt/double-matching/blob/HEAD/code/MultiAgent.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"52aa97f6d9204e6c"}},{"code_sha256_prefix":"da204097cd0b01b8","entry":"Policy","repo":"likelyt/double-matching","repo_kind":"official","path":"code/MultiAgent.py","file_url":"https://github.com/likelyt/double-matching/blob/HEAD/code/MultiAgent.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"da204097cd0b01b8"}},{"code_sha256_prefix":"425cf9caad5c8c0d","entry":"School_Choice_Algo","repo":"likelyt/double-matching","repo_kind":"official","path":"code/MultiAgent.py","file_url":"https://github.com/likelyt/double-matching/blob/HEAD/code/MultiAgent.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"425cf9caad5c8c0d"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}