Welfarist Formulations for Diverse Similarity Search

TL;DR

This paper introduces welfare-based formulations for diverse similarity search that balance relevance and diversity using economic welfare functions, enabling flexible, query-dependent trade-offs with provable algorithms and practical improvements.

Contribution

It proposes a novel welfare-based framework for diversity in nearest neighbor search, integrating economic principles to adaptively balance relevance and diversity, unlike prior fixed-constraint methods.

Findings

Improves diversity of search results significantly.

Maintains high relevance while enhancing diversity.

Provides provable algorithms compatible with standard ANN methods.

Abstract

Nearest Neighbor Search (NNS) is a fundamental problem in data structures with wide-ranging applications, such as web search, recommendation systems, and, more recently, retrieval-augmented generations (RAG). In such recent applications, in addition to the relevance (similarity) of the returned neighbors, diversity among the neighbors is a central requirement. In this paper, we develop principled welfare-based formulations in NNS for realizing diversity across attributes. Our formulations are based on welfare functions -- from mathematical economics -- that satisfy central diversity (fairness) and relevance (economic efficiency) axioms. With a particular focus on Nash social welfare, we note that our welfare-based formulations provide objective functions that adaptively balance relevance and diversity in a query-dependent manner. Notably, such a balance was not present in the prior constraint-based approach, which forced a fixed level of diversity and optimized for relevance. In addition, our formulation provides a parametric way to control the trade-off between relevance and diversity, providing practitioners with flexibility to tailor search results to task-specific requirements. We develop efficient nearest neighbor algorithms with provable guarantees for the welfare-based objectives. Notably, our algorithm can be applied on top of any standard ANN method (i.e., use standard ANN method as a subroutine) to efficiently find neighbors that approximately maximize our welfare-based objectives. Experimental results demonstrate that our approach is practical and substantially improves diversity while maintaining high relevance of the retrieved neighbors.