Trading Vector Data in Vector Databases

TL;DR

This paper introduces a hierarchical bandit framework for trading vector data in vector databases, jointly optimizing retrieval configurations and pricing to handle uncertain feedback and improve overall performance.

Contribution

It presents a novel hierarchical bandit approach that combines configuration learning and pricing optimization with theoretical guarantees and real-world validation.

Findings

Achieves logarithmic regret in configuration learning.

Attains sublinear regret in pricing optimization.

Demonstrates consistent reward improvements on real datasets.

Abstract

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.