{"paper":{"title":"Stochastic Linear Bandits with Parameter Noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Alon Peled-Cohen, Daniel Ezer, Yishay Mansour","submitted_at":"2026-01-30T16:47:42Z","abstract_excerpt":"We study the stochastic linear bandits with parameter noise model, in which the reward of action $a$ is $a^\\top \\theta$ where $\\theta$ is sampled i.i.d. We show a regret upper bound of $\\widetilde{O} (\\sqrt{d T \\log (K/\\delta) \\sigma^2_{\\max})}$ for a horizon $T$, general action set of size $K$ of dimension $d$, and where $\\sigma^2_{\\max}$ is the maximal variance of the reward for any action. We further provide a lower bound of $\\widetilde{\\Omega} (d \\sqrt{T \\sigma^2_{\\max}})$ which is tight (up to logarithmic factors) whenever $\\log (K) \\approx d$. For more specific action sets, $\\ell_p$ unit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.23164","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.23164/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}