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Principled and Scalable Diversity-Aware Retrieval via Cardinality-Constrained Binary Quadratic Programming

Qiheng Lu, Nicholas D. Sidiropoulos

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.

Principled and Scalable Diversity-Aware Retrieval via Cardinality-Constrained Binary Quadratic Programming

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 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.

Paper Structure

This paper contains 14 sections, 5 theorems, 26 equations, 1 figure, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Optimization Algorithm
  4. Experiments
  5. Experimental Setup
  6. Retrieval Experiments
  7. Generation Experiments
  8. Discussion
  9. Conclusion
  10. Proof of Theorem \ref{['thm1']}
  11. Proof of Theorem \ref{['thm2']}
  12. Proof of Theorem \ref{['thm3']}
  13. Proof of Theorem \ref{['thm4']}
  14. Generation results for ASQA

Key Result

Theorem 2.1

If $\lambda \geq 2$, the relaxation from p2 to p3 is tight for any $k$. $\blacktriangleleft$$\blacktriangleleft$

Figures (1)

  • Figure 1: Relevance-diversity trade-off and efficiency. Relevance-diversity trade-off and computational efficiency on ASQA and QAMPARI across $k \in \{25, 50, 100\}$. The left panels show the Pareto frontier of Recall vs. ILAD by modulating the trade-off parameter $\theta \in [0.1, 0.9]$. The right panels report the per-query wall-clock latency (ms). Our algorithm consistently yields superior subset quality and significant speedup.

Theorems & Definitions (13)

  • Theorem 2.1
  • proof
  • Corollary 2.3
  • Theorem 2.4: Strict Dichotomy of Stationary Points
  • proof
  • Theorem 2.5: Monotonicity of Local Maximizers
  • proof
  • Theorem 3.1: Local Exact Convergence
  • proof
  • proof
  • ...and 3 more