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.

翻译：多样性感知检索对于检索增强生成（RAG）至关重要，然而现有方法缺乏理论保证，且随着检索段落数量 $k$ 的增加面临可扩展性问题。我们提出一种将多样性检索形式化为基数约束二元二次规划（CCBQP）的原则性方法，该方法通过一个可解释的权衡参数显式平衡相关性与语义多样性。受组合优化最新进展的启发，我们开发了一种非凸紧连续松弛方法以及基于Frank-Wolfe的算法，该算法具备景观分析与收敛性保证。大量实验表明，我们的方法在相关性-多样性帕累托前沿上始终优于基线方法，同时实现了显著的加速。