Efficient Algorithms for Adversarially Robust Approximate Nearest Neighbor Search

2026-01-01

arXiv.org

AI Summary

This work addresses approximate nearest neighbor (ANN) search in adaptive adversarial settings, distinguishing between high-dimensional regimes (\(d = \omega(\sqrt{Q})\)) and low-dimensional ones (\(d = O(\sqrt{Q})\)). The paper proposes a novel algorithm that integrates differential privacy, fairness, and locality-sensitive hashing (LSH). Its key contributions include establishing the first theoretical connection between adaptive security and fairness, introducing a concentric-ring LSH structure that overcomes the traditional \(\sqrt{n}\) query time barrier, and incorporating robust decision primitives with metric covering techniques. In high dimensions, the method achieves information-theoretically secure and efficient search; in low dimensions, it guarantees— with high probability—“all-or-nothing” correctness for arbitrary queries, substantially outperforming existing approaches.

Technology Category

• Search and Optimization: Adversarial Search
• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

We study the Approximate Nearest Neighbor (ANN) problem under a powerful adaptive adversary that controls both the dataset and a sequence of $Q$ queries. Primarily, for the high-dimensional regime of $d = \omega(\sqrt{Q})$, we introduce a sequence of algorithms with progressively stronger guarantees. We first establish a novel connection between adaptive security and \textit{fairness}, leveraging fair ANN search to hide internal randomness from the adversary with information-theoretic guarantees. To achieve data-independent performance, we then reduce the search problem to a robust decision primitive, solved using a differentially private mechanism on a Locality-Sensitive Hashing (LSH) data structure. This approach, however, faces an inherent $\sqrt{n}$ query time barrier. To break the barrier, we propose a novel concentric-annuli LSH construction that synthesizes these fairness and differential privacy techniques. The analysis introduces a new method for robustly releasing timing information from the underlying algorithm instances and, as a corollary, also improves existing results for fair ANN. In addition, for the low-dimensional regime $d = O(\sqrt{Q})$, we propose specialized algorithms that provide a strong ``for-all''guarantee: correctness on \textit{every} possible query with high probability. We introduce novel metric covering constructions that simplify and improve prior approaches for ANN in Hamming and $\ell_p$ spaces.

Problem

• Adversarially Robust
• Approximate Nearest Neighbor
• Adaptive Adversary
• High-dimensional Search
• Fairness

Innovation

• adversarially robust
• fairness
• differential privacy
• locality-sensitive hashing
• metric covering