arXiv:2601.09162cs.LGstat.ML2026-01被引 1

提出高效聚类算法,实现快速且准确的随机多臂问题聚类。

Efficient Clustering in Stochastic Bandits

  • 采用单步优化近似替代全优化,显著降低计算开销。
  • 在合成与真实数据集上均优于现有方法,保持渐近最优性。
  • 适合需要实时响应的在线聚类场景,如动态推荐系统。

我们研究在固定置信度设置下的多臂聚类(BC)问题,目标是在保证停止时刻误差概率固定的条件下,通过自适应选择臂进行序列采样,将一组数据序列(臂)分组为簇。考虑簇内臂具有不同分布的情形,突破了以往仅限于高斯分布的假设,扩展到满足弱正则条件的向量参数分布。现有渐近最优的BC算法需在每一步求解优化问题,计算成本高。本文提出高效多臂聚类算法(EBC),不求解完整优化问题,而是每步仅向最优值迈进一步,兼顾计算效率与渐近最优性。还提出启发式变体EBC-H,其臂选择基于停止规则中已计算量,进一步简化。通过对比运行时间验证了EBC和EBC-H的高效性。仿真结果表明,二者在合成与真实数据集上性能优于现有方法,且渐近最优性得到支持。

原文摘要 · Abstract (English)

We study the Bandit Clustering (BC) problem under the fixed confidence setting, where the objective is to group a collection of data sequences (arms) into clusters through sequential sampling from adaptively selected arms at each time step while ensuring a fixed error probability at the stopping time. We consider a setting where arms in a cluster may have different distributions. Unlike existing results in this setting, which assume Gaussian-distributed arms, we study a broader class of vector-parametric distributions that satisfy mild regularity conditions. Existing asymptotically optimal BC algorithms require solving an optimization problem as part of their sampling rule at each step, which is computationally costly. We propose an Efficient Bandit Clustering algorithm (EBC), which, instead of solving the full optimization problem, takes a single step toward the optimal value at each time step, making it computationally efficient while remaining asymptotically optimal. We also propose a heuristic variant of EBC, called EBC-H, which further simplifies the sampling rule, with arm selection based on quantities computed as part of the stopping rule. We highlight the computational efficiency of EBC and EBC-H by comparing their per-sample run time with that of existing algorithms. The asymptotic optimality of EBC is supported through simulations on the synthetic datasets. Through simulations on both synthetic and real-world datasets, we show the performance gain of EBC and EBC-H over existing approaches.

多臂问题聚类算法高效计算

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