Greedy Algorithm for Structured Bandits: A Sharp Characterization of Asymptotic Success / Failure
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918189526417408 |
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| author | Slivkins, Aleksandrs Xu, Yunzong Zuo, Shiliang |
| author_facet | Slivkins, Aleksandrs Xu, Yunzong Zuo, Shiliang |
| contents | We study the greedy (exploitation-only) algorithm in bandit problems with a known reward structure. We allow arbitrary finite reward structures, while prior work focused on a few specific ones. We fully characterize when the greedy algorithm asymptotically succeeds or fails, in the sense of sublinear vs. linear regret as a function of time. Our characterization identifies a partial identifiability property of the problem instance as the necessary and sufficient condition for the asymptotic success. Notably, once this property holds, the problem becomes easy -- any algorithm will succeed (in the same sense as above), provided it satisfies a mild non-degeneracy condition. Our characterization extends to contextual bandits and interactive decision-making with arbitrary feedback. Examples demonstrating broad applicability and extensions to infinite reward structures are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04010 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Greedy Algorithm for Structured Bandits: A Sharp Characterization of Asymptotic Success / Failure Slivkins, Aleksandrs Xu, Yunzong Zuo, Shiliang Machine Learning Data Structures and Algorithms We study the greedy (exploitation-only) algorithm in bandit problems with a known reward structure. We allow arbitrary finite reward structures, while prior work focused on a few specific ones. We fully characterize when the greedy algorithm asymptotically succeeds or fails, in the sense of sublinear vs. linear regret as a function of time. Our characterization identifies a partial identifiability property of the problem instance as the necessary and sufficient condition for the asymptotic success. Notably, once this property holds, the problem becomes easy -- any algorithm will succeed (in the same sense as above), provided it satisfies a mild non-degeneracy condition. Our characterization extends to contextual bandits and interactive decision-making with arbitrary feedback. Examples demonstrating broad applicability and extensions to infinite reward structures are provided. |
| title | Greedy Algorithm for Structured Bandits: A Sharp Characterization of Asymptotic Success / Failure |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2503.04010 |