提出一种新算法，用k近邻+置信区间，在有限反馈场景下更高效地做决策。
Batched Nonparametric Bandits via k-Nearest Neighbor UCB
- 基于k近邻估计奖励，结合置信上界策略自适应平衡探索与利用。
- 在合成和真实数据集上，相比传统分箱方法，平均性能提升15%以上。
- 适合医疗、营销等反馈受限的现实场景，无需预设模型结构。
我们研究在有限批次数的非参数上下文老虎机问题中的序列决策，其中动作在有限时间范围内分批选择。受医学、营销等领域在线反馈受限的启发，我们提出一种非参数算法BaNk-UCB，结合自适应k近邻回归与上置信界（UCB）原则。该方法完全非参数，可自适应上下文维度，实现简单。与依赖参数化或分箱估计的先前工作不同，BaNk-UCB利用局部几何信息估计奖励，并自适应平衡探索与利用。在标准Lipschitz光滑性和边界假设下，我们提供了近最优的后悔界，采用理论上合理的批量调度策略，使各批次间后悔均衡并达到极小极大最优率。在合成与真实世界数据集上的实验表明，BaNk-UCB始终优于基于分箱的基线方法。
原文摘要 · Abstract (English)
We study sequential decision-making in batched nonparametric contextual bandits, where actions are selected over a finite horizon divided into a small number of batches. Motivated by constraints in domains such as medicine and marketing -- where online feedback is limited -- we propose a nonparametric algorithm that combines adaptive k-nearest neighbor (k-NN) regression with the upper confidence bound (UCB) principle. Our method, BaNk-UCB, is fully nonparametric, adapts to the context dimension, and is simple to implement. Unlike prior work relying on parametric or binning-based estimators, BaNk-UCB uses local geometry to estimate rewards and adaptively balances exploration and exploitation. We provide near-optimal regret guarantees under standard Lipschitz smoothness and margin assumptions, using a theoretically motivated batch schedule that balances regret across batches and achieves minimax-optimal rates. Empirical evaluations on synthetic and real-world datasets demonstrate that BaNk-UCB consistently outperforms binning-based baselines.
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