{"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/non-monotonic-resource-utilization-in-the","title":"Non-monotonic Resource Utilization in the Bandits with Knapsacks Problem","arxiv_id":"2209.12013","date":"2022-09-24","proceeding":null,"authors":["Raunak Kumar","Robert Kleinberg"],"abstract":"Bandits with knapsacks (BwK) is an influential model of sequential decision-making under uncertainty that incorporates resource consumption constraints. In each round, the decision-maker observes an outcome consisting of a reward and a vector of nonnegative resource consumptions, and the budget of each resource is decremented by its consumption. In this paper we introduce a natural generalization of the stochastic BwK problem that allows non-monotonic resource utilization. In each round, the decision-maker observes an outcome consisting of a reward and a vector of resource drifts that can be positive, negative or zero, and the budget of each resource is incremented by its drift. Our main result is a Markov decision process (MDP) policy that has constant regret against a linear programming (LP) relaxation when the decision-maker knows the true outcome distributions. We build upon this to develop a learning algorithm that has logarithmic regret against the same LP relaxation when the decision-maker does not know the true outcome distributions. We also present a reduction from BwK to our model that shows our regret bound matches existing results.","url_abs":"https://arxiv.org/abs/2209.12013v1","url_pdf":"https://arxiv.org/pdf/2209.12013v1.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":"non-monotonic-resource-utilization-in-the","repo_url":"https://github.com/raunakkmr/non-monotonic-resource-utilization-in-the-bandits-with-knapsacks-problem-code","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"decision-making","task_name":"Decision Making"},{"task_slug":"decision-making-under-uncertainty","task_name":"Decision Making Under Uncertainty"},{"task_slug":"sequential-decision-making","task_name":"Sequential Decision Making"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2209.12013","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2209.12013"}},"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/raunakkmr/non-monotonic-resource-utilization-in-the-bandits-with-knapsacks-problem-code","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":2},"by_repo_kind":{"official":{"samples":2,"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":0,"samples":[{"code_sha256_prefix":"b9d572953218eac1","entry":"compute_support","repo":"raunakkmr/non-monotonic-resource-utilization-in-the-bandits-with-knapsacks-problem-code","repo_kind":"official","path":"src/algorithms.py","file_url":"https://github.com/raunakkmr/non-monotonic-resource-utilization-in-the-bandits-with-knapsacks-problem-code/blob/HEAD/src/algorithms.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b9d572953218eac1"}},{"code_sha256_prefix":"f0ac63597e60faa6","entry":"parse_datafile","repo":"raunakkmr/non-monotonic-resource-utilization-in-the-bandits-with-knapsacks-problem-code","repo_kind":"official","path":"src/data.py","file_url":"https://github.com/raunakkmr/non-monotonic-resource-utilization-in-the-bandits-with-knapsacks-problem-code/blob/HEAD/src/data.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f0ac63597e60faa6"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}