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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

Japanese

私たちは、ポジション依存コストが発生し、学習者はそれぞれの腕の実際の出力についてだけ騒音のフィードバックを観察します。私たちは、各腕のスコアに基づいて腕のスコアを分類することで最適なスコアリストを見つけることができるノウハウモデルのサブクラスを特定します:このスコアは、チャンネルが偽ポジティブを持たない場合の選択と注文の両方のために存在します、そして、測定が無料である場合の単独注文(しかし選択ではありません)のために存在します。しかし、一般的には、ノウハウとコストの両方が存在するときの選択と注文のスコアを分離することはできません。両方が存在する場合、UCBベースのアルゴリズムを提供します $O(L-Klog)\T$

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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