{"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/on-the-optimality-of-perturbations-in","title":"On the Optimality of Perturbations in Stochastic and Adversarial Multi-armed Bandit Problems","arxiv_id":"1902.00610","date":"2019-02-02","proceeding":"NeurIPS 2019 12","authors":["Baekjin Kim","Ambuj Tewari"],"abstract":"We investigate the optimality of perturbation based algorithms in the stochastic and adversarial multi-armed bandit problems. For the stochastic case, we provide a unified regret analysis for both sub-Weibull and bounded perturbations when rewards are sub-Gaussian. Our bounds are instance optimal for sub-Weibull perturbations with parameter 2 that also have a matching lower tail bound, and all bounded support perturbations where there is sufficient probability mass at the extremes of the support. For the adversarial setting, we prove rigorous barriers against two natural solution approaches using tools from discrete choice theory and extreme value theory. Our results suggest that the optimal perturbation, if it exists, will be of Frechet-type.","url_abs":"https://arxiv.org/abs/1902.00610v4","url_pdf":"https://arxiv.org/pdf/1902.00610v4.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":"on-the-optimality-of-perturbations-in","repo_url":"https://github.com/Kimbaekjin/Perturbation-Methods-StochasticMAB","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"on-the-optimality-of-perturbations-in","repo_url":"https://github.com/baekjin-kim/Perturbation-Methods-StochasticMAB","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1902.00610","atlas_url":"https://app.syntology.ai/?focus=1902.00610","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1902.00610"}},"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/Kimbaekjin/Perturbation-Methods-StochasticMAB","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/baekjin-kim/Perturbation-Methods-StochasticMAB","reach":null}],"summary":{"ran_honours":3},"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":"6ec138954b1de3c6","entry":"reward_generate","repo":"baekjin-kim/Perturbation-Methods-StochasticMAB","repo_kind":"official","path":"experiments.py","file_url":"https://github.com/baekjin-kim/Perturbation-Methods-StochasticMAB/blob/HEAD/experiments.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"6ec138954b1de3c6"}},{"code_sha256_prefix":"99b6a0fdb71529c7","entry":"reward_generate","repo":"baekjin-kim/Perturbation-Methods-StochasticMAB","repo_kind":"official","path":"experiments.py","file_url":"https://github.com/baekjin-kim/Perturbation-Methods-StochasticMAB/blob/HEAD/experiments.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"99b6a0fdb71529c7"}},{"code_sha256_prefix":"95d6a7b81669865c","entry":"reward_generate","repo":"baekjin-kim/Perturbation-Methods-StochasticMAB","repo_kind":"official","path":"experiments.py","file_url":"https://github.com/baekjin-kim/Perturbation-Methods-StochasticMAB/blob/HEAD/experiments.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"95d6a7b81669865c"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}