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We report significant progress in addressing this issue for linear bandits in two respects. First, we propose a novel confidence set that is `semi-adaptive' to the unknown sub-Gaussian parameter $\\sigma_*^2$ in the sense that the (normalized) confidence width scales with $\\sqrt{d\\sigma_*^2 + \\sigma_0^2}$ where $d$ is the dimension and $\\sigma_0^2$ is the specified sub-Gaussian parameter (known) that can be much larger than $\\sigma_*^2$. This is a significant improvement over $\\sqrt{d\\sigma_0^2}$ of the standard confidence set of Abbasi-Yadkori et al. (2011), especially when $d$ is large or $\\sigma_*^2=0$. We show that this leads to an improved regret bound in linear bandits. Second, for bounded rewards, we propose a novel variance-adaptive confidence set that has much improved numerical performance upon prior art. We then apply this confidence set to develop, as we claim, the first practical variance-adaptive linear bandit algorithm via an optimistic approach, which is enabled by our novel regret analysis technique. Both of our confidence sets rely critically on `regret equality' from online learning. Our empirical evaluation in diverse Bayesian optimization tasks shows that our proposed algorithms demonstrate better or comparable performance compared to existing methods.","url_abs":"https://arxiv.org/abs/2402.07341v2","url_pdf":"https://arxiv.org/pdf/2402.07341v2.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":"noise-adaptive-confidence-sets-for-linear","repo_url":"https://github.com/jungtaekkim/losan-lofav","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"bayesian-optimization","task_name":"Bayesian Optimization"},{"task_slug":"decision-making","task_name":"Decision Making"},{"task_slug":"efficient-exploration","task_name":"Efficient Exploration"},{"task_slug":"sequential-decision-making","task_name":"Sequential Decision Making"}],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2402.07341","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2402.07341"}},"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. 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