在数据稀缺下解决稀疏线性博弈的唯一访问约束问题,提升推荐与标注效率。
Sparse Linear Bandits with Blocking Constraints
- 设计在线算法BSLB,在每臂仅可选一次的限制下优化决策。
- 理论证明算法累计误差为约T^{2/3}量级,优于传统方法。
- 无需预知最优稀疏度,适合实际推荐与数据标注场景。
我们研究高维稀疏线性贝叶斯问题在数据贫乏场景下的表现,即时间范围远小于环境维度和臂的数量。在此背景下引入唯一访问约束(每种臂只能被选取一次),该约束源于个性化内容推荐及复杂学习任务中提高标注效率的实际需求。在对臂的温和假设下,所提出的在线算法BSLB实现$ ilde{ ext{O}}((1+β_k)^2k^{2/3} ext{T}^{2/3})$的累积后悔界,其中参数向量的相对尾部衰减系数$β_k$为前$k$个非零分量与其余分量的$ ext{l}_1$范数比值。为此,我们给出了对线性模型中套索估计器的新颖离线统计保证,且对稀疏建模假设具有鲁棒性。最后,提出基于协同策略的元算法C-BSLB,无需已知最优稀疏度$k$,且几乎不增加后悔量。多个真实数据集上的实验验证了算法与理论框架的有效性。
原文摘要 · Abstract (English)
We investigate the high-dimensional sparse linear bandits problem in a data-poor regime where the time horizon is much smaller than the ambient dimension and number of arms. We study the setting under the additional blocking constraint where each unique arm can be pulled only once. The blocking constraint is motivated by practical applications in personalized content recommendation and identification of data points to improve annotation efficiency for complex learning tasks. With mild assumptions on the arms, our proposed online algorithm (BSLB) achieves a regret guarantee of $\widetilde{\mathsf{O}}((1+β_k)^2k^{\frac{2}{3}} \mathsf{T}^{\frac{2}{3}})$ where the parameter vector has an (unknown) relative tail $β_k$ -- the ratio of $\ell_1$ norm of the top-$k$ and remaining entries of the parameter vector. To this end, we show novel offline statistical guarantees of the lasso estimator for the linear model that is robust to the sparsity modeling assumption. Finally, we propose a meta-algorithm (C-BSLB) based on corralling that does not need knowledge of optimal sparsity parameter $k$ at minimal cost to regret. Our experiments on multiple real-world datasets demonstrate the validity of our algorithms and theoretical framework.
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