Newest papers

Cascading Bandits with Noisy Observations: Algorithms and Regret Bounds

Yashaswini Kaluguri, Nikhil Karamchandani · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29381 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

我們提出了一個新的斯托加斯特式滑坡破壞者設定,在那裡調查一個順序的短列 $K$ 從 $L$ 武器會產生位置依賴的成本,而學習者只觀察到關於每個手臂真正的輸出的噪音反應。我們識別出一個噪音模型的子類,其中最佳短列可以通過按每個手臂的分類來找到:這樣的分數既存在於選擇和訂單時,當渠道沒有虛假陽性,而且僅存在於單獨訂單(但不選擇)時,當測量是免費的;然而,一般來說,當噪音和成本都存在時,既沒有選擇,也沒有訂單可以分離。如果有兩個手臂按每個手臂分類和訂單得分數,我們提供一個基於UCB

Machine translation (Meta M2M100); the English original follows.

Abstract

We propose a novel stochastic cascading bandit setup where probing an ordered shortlist of $K$ out of $L$ arms incurs position-dependent costs, and the learner observes only noisy feedback regarding each arm's true output. We identify a sub-class of noise models for which the optimal shortlist can be found by sorting arms according to a per-arm score: such a score exists for both selection and ordering when the channel has no false positives, and for ordering alone (but not selection) when measurements are costless; however in general neither selection nor ordering is separable once noise and cost are both present. For the case where both selection and ordering scores exist, we provide a UCB-based algorithm with $O((L-K)\log T)$ instance-dependent regret over a time horizon $T$, which matches an algorithm-agnostic lower bound (up to constant factors). For the more challenging scenario where scores don't exist, we develop a new algorithmic template, DP-UCB, that embeds optimism directly inside an exact dynamic program, yielding $O\big(LK\log T\big)$ regret. Finally, we validate our theoretical results through extensive numerical evaluations and simulations over both synthetic and real-world datasets.

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Topics: Regret, Algorithm, Selection (genetic algorithm), Noise (video), Sorting, Upper and lower bounds

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