{"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/planning-to-fairly-allocate-probabilistic","title":"Planning to Fairly Allocate: Probabilistic Fairness in the Restless Bandit Setting","arxiv_id":"2106.07677","date":"2021-06-14","proceeding":null,"authors":["Christine Herlihy","Aviva Prins","Aravind Srinivasan","John P. Dickerson"],"abstract":"Restless and collapsing bandits are often used to model budget-constrained resource allocation in settings where arms have action-dependent transition probabilities, such as the allocation of health interventions among patients. However, state-of-the-art Whittle-index-based approaches to this planning problem either do not consider fairness among arms, or incentivize fairness without guaranteeing it. We thus introduce ProbFair, a probabilistically fair policy that maximizes total expected reward and satisfies the budget constraint while ensuring a strictly positive lower bound on the probability of being pulled at each timestep. We evaluate our algorithm on a real-world application, where interventions support continuous positive airway pressure (CPAP) therapy adherence among patients, as well as on a broader class of synthetic transition matrices. We find that ProbFair preserves utility while providing fairness guarantees.","url_abs":"https://arxiv.org/abs/2106.07677v4","url_pdf":"https://arxiv.org/pdf/2106.07677v4.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":"planning-to-fairly-allocate-probabilistic","repo_url":"https://github.com/crherlihy/prob_fair_rmab","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"fairness","task_name":"Fairness"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2106.07677","atlas_url":"https://app.syntology.ai/?focus=2106.07677","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2106.07677"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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/crherlihy/prob_fair_rmab","reach":null}],"summary":{"ran_violates":1,"ran_draft_wrong":1,"ran_fixture":1},"by_repo_kind":{"official":{"samples":3,"ran":3,"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":"c5d9372489b7f562","entry":"compute_ib","repo":"crherlihy/prob_fair_rmab","repo_kind":"official","path":"src/Analysis/generate_figures.py","file_url":"https://github.com/crherlihy/prob_fair_rmab/blob/HEAD/src/Analysis/generate_figures.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"GPL-3.0","inline_ok":false,"mcp_get_code":{"code_sha256":"c5d9372489b7f562"}},{"code_sha256_prefix":"a8087b33973c8f2e","entry":"map_adherences_to_localr","repo":"crherlihy/prob_fair_rmab","repo_kind":"official","path":"src/Analysis/generate_figures.py","file_url":"https://github.com/crherlihy/prob_fair_rmab/blob/HEAD/src/Analysis/generate_figures.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"GPL-3.0","inline_ok":false,"mcp_get_code":{"code_sha256":"a8087b33973c8f2e"}},{"code_sha256_prefix":"c52f2dfaef7931bb","entry":"map_localr_to_R","repo":"crherlihy/prob_fair_rmab","repo_kind":"official","path":"src/Analysis/generate_figures.py","file_url":"https://github.com/crherlihy/prob_fair_rmab/blob/HEAD/src/Analysis/generate_figures.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"GPL-3.0","inline_ok":false,"mcp_get_code":{"code_sha256":"c52f2dfaef7931bb"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}