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arXiv · 2503.04010

Greedy Algorithm for Structured Bandits: A Sharp Characterization of Asymptotic Success / Failure

Aleksandrs Slivkins·Yunzong Xu·Shiliang Zuo
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Abstract

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.

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Aleksandrs Slivkins, Yunzong Xu, Shiliang Zuo. 2025-03-06. Greedy Algorithm for Structured Bandits: A Sharp Characterization of Asymptotic Success / Failure. https://arxiv.org/abs/2503.04010

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