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Current literature typically assumes that the tasks are diverse, i.e., their parameters uniformly span the $m$-dimensional subspace. This assumption allows the low-rank representation to be learned before all tasks are revealed, which can be unrealistic in real-world applications. In this work, we present the first nontrivial result for sequential multi-task linear bandits without the task diversity assumption. We develop an algorithm that efficiently learns and transfers low-rank representations. When facing $N$ tasks, each played over $\\tau$ rounds, our algorithm achieves a regret guarantee of $\\tilde{O}\\big (Nm \\sqrt{\\tau} + N^{\\frac{2}{3}} \\tau^{\\frac{2}{3}} d m^{\\frac13} + Nd^2 + \\tau m d \\big)$ under the ellipsoid action set assumption. This result can significantly improve upon the baseline of $\\tilde{O} \\left (Nd \\sqrt{\\tau}\\right)$ that does not leverage the low-rank structure when the number of tasks $N$ is sufficiently large and $m \\ll d$. We also demonstrate empirically on synthetic data that our algorithm outperforms baseline algorithms, which rely on the task diversity assumption.","url_abs":"https://arxiv.org/abs/2501.13390v1","url_pdf":"https://arxiv.org/pdf/2501.13390v1.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":"beyond-task-diversity-provable-representation","repo_url":"https://github.com/duongnhatthang/BOSS","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"diversity","task_name":"Diversity"},{"task_slug":"lifelong-learning","task_name":"Lifelong learning"}],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2501.13390","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2501.13390"}},"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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