提出分层强化学习框架，优化向量数据库的配置与定价。
Trading Vector Data in Vector Databases
- 分两阶段优化：先聚类配置，再基于价格区间逼近买家响应。
- 在四个真实数据集上实现累积收益提升与后悔值降低。
- 适用于需要动态定价和配置的向量数据交易场景。
向量数据交易对跨领域学习至关重要，但目前仍缺乏研究。本文在在线学习设定下研究该问题，卖家面临不确定的检索成本，买家对定价提供随机反馈。主要挑战包括：(1) 配置学习中的异构且不完整的反馈；(2) 定价学习中可变复杂的反馈；(3) 配置与定价决策间的固有耦合。我们提出一种分层贝叶斯框架，联合优化检索配置与定价策略。第一阶段采用带置信度探索的上下文聚类，实现对数后悔率；第二阶段采用基于区间的定价选择与局部泰勒近似，估计买家响应并达到次线性后悔率。理论分析表明该框架具有多项式时间复杂度，并在四个真实数据集上验证了其有效性，相较现有方法显著提升了累积奖励并降低了后悔值。
原文摘要 · Abstract (English)
Vector data trading is essential for cross-domain learning with vector databases, yet it remains largely unexplored. We study this problem under online learning, where sellers face uncertain retrieval costs and buyers provide stochastic feedback to posted prices. Three main challenges arise: (1) heterogeneous and partial feedback in configuration learning, (2) variable and complex feedback in pricing learning, and (3) inherent coupling between configuration and pricing decisions. We propose a hierarchical bandit framework that jointly optimizes retrieval configurations and pricing. Stage I employs contextual clustering with confidence-based exploration to learn effective configurations with logarithmic regret. Stage II adopts interval-based price selection with local Taylor approximation to estimate buyer responses and achieve sublinear regret. We establish theoretical guarantees with polynomial time complexity and validate the framework on four real-world datasets, demonstrating consistent improvements in cumulative reward and regret reduction compared with existing methods.
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