Preference-based Pure Exploration

Apurv Shukla; Debabrota Basu

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arXiv · 2412.02988

Preference-based Pure Exploration

Apurv Shukla·Debabrota Basu

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Abstract

We study the preference-based pure exploration problem for bandits with vector-valued rewards. The rewards are ordered using a (given) preference cone $\mathcal{C}$ and our goal is to identify the set of Pareto optimal arms. First, to quantify the impact of preferences, we derive a novel lower bound on sample complexity for identifying the most preferred policy with a confidence level $1-\delta$. Our lower bound elicits the role played by the geometry of the preference cone and punctuates the difference in hardness compared to existing best-arm identification variants of the problem. We further explicate this geometry when the rewards follow Gaussian distributions. We then provide a convex relaxation of the lower bound and leverage it to design the Preference-based Track and Stop (PreTS) algorithm that identifies the most preferred policy. Finally, we show that the sample complexity of PreTS is asymptotically tight by deriving a new concentration inequality for vector-valued rewards.

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Apurv Shukla, Debabrota Basu. 2024-12-04. Preference-based Pure Exploration. https://arxiv.org/abs/2412.02988

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