Clustering-based nearest neighbor search is a simple yet effective method in which data points are partitioned into geometric shards to form an index, and only a few shards are searched during query processing to find an approximate set of top-$k$ vectors. Even though the search efficacy is heavily influenced by the algorithm that identifies the set of shards to probe, it has received little attention in the literature. This work attempts to bridge that gap by studying the problem of routing in clustering-based maximum inner product search (MIPS). We begin by unpacking existing routing protocols and notice the surprising contribution of optimism. We then take a page from the sequential decision making literature and formalize that insight following the principle of ``optimism in the face of uncertainty.'' In particular, we present a new framework that incorporates the moments of the distribution of inner products within each shard to optimistically estimate the maximum inner product. We then present a simple instance of our algorithm that uses only the first two moments to reach the same accuracy as state-of-the-art routers such as \scann by probing up to $50%$ fewer points on a suite of benchmark MIPS datasets. Our algorithm is also space-efficient: we design a sketch of the second moment whose size is independent of the number of points and in practice requires storing only $O(1)$ additional vectors per shard.

本研究旨在研究基于聚类的最近邻搜索中路由问题，通过乐观主义的原则，利用内积分布的矩来乐观地估计最大内积，通过只使用前两个矩实现与现有算法相当准确度的搜索，并且所提出的算法在空间利用上也更为高效。

基于聚类的近似最大内积搜索中的乐观查询路由