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Poster

Lipschitz Bandits with Batched Feedback

Yasong Feng · zengfeng Huang · Tianyu Wang

Keywords: [ batched bandits ] [ Lipschitz bandits ]


Abstract: In this paper, we study Lipschitz bandit problems with batched feedback, where the expected reward is Lipschitz and the reward observations are communicated to the player in batches. We introduce a novel landscape-aware algorithm, called Batched Lipschitz Narrowing (BLiN), that optimally solves this problem. Specifically, we show that for a T-step problem with Lipschitz reward of zooming dimension dz, our algorithm achieves theoretically optimal (up to logarithmic factors) regret rate O~(Tdz+1dz+2) using only O(loglogT) batches. We also provide complexity analysis for this problem. Our theoretical lower bound implies that Ω(loglogT) batches are necessary for any algorithm to achieve the optimal regret. Thus, BLiN achieves optimal regret rate using minimal communication.

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