🤖 AI Summary
This work addresses the challenge that existing retrieval methods lack theoretical guarantees when scaling up and struggle to balance relevance and semantic diversity. The authors formulate diversity-aware retrieval as a cardinality-constrained binary quadratic programming problem, introducing an interpretable parameter to explicitly trade off between relevance and diversity. They propose, for the first time, a scalable optimization framework with provable convergence guarantees, which combines a non-convex tight continuous relaxation with the Frank-Wolfe algorithm to enable efficient solution. Experimental results demonstrate that the proposed method consistently outperforms existing baselines across the relevance-diversity Pareto frontier while achieving substantial gains in computational efficiency.
📝 Abstract
Diversity-aware retrieval is essential for Retrieval-Augmented Generation (RAG), yet existing methods lack theoretical guarantees and face scalability issues as the number of retrieved passages $k$ increases. We propose a principled formulation of diversity retrieval as a cardinality-constrained binary quadratic programming (CCBQP), which explicitly balances relevance and semantic diversity through an interpretable trade-off parameter. Inspired by recent advances in combinatorial optimization, we develop a non-convex tight continuous relaxation and a Frank--Wolfe based algorithm with landscape analysis and convergence guarantees. Extensive experiments demonstrate that our method consistently dominates baselines on the relevance-diversity Pareto frontier, while achieving significant speedup.