Adaptively Robust Resettable Streaming

2026-01-29

AI Summary

This work addresses the vulnerability of existing reset-stream algorithms under adaptive adversarial attacks, where correctness cannot be guaranteed even with polynomial space. Focusing on the reset-stream model that supports key-value increments or resets to zero, the paper presents the first streaming algorithm that simultaneously achieves adaptive robustness and logarithmic-polynomial space complexity, thereby overcoming the theoretical limitations of linearly composable sketches. By integrating differential privacy with the Binary Tree Mechanism to jointly protect the internal randomness of sketches, the proposed method enables accurate estimation of $L_p$ moments for $p \in [0,1]$ and Bernstein statistics, while providing rigorous guarantees on prefix maximum error. The algorithm operates within polylogarithmic space relative to the stream length, significantly outperforming existing approaches.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Data Mining & Knowledge Management: Data Stream Mining
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Algorithmic accountability and transparency on the web

Abstract

We study algorithms in the resettable streaming model, where the value of each key can either be increased or reset to zero. The model is suitable for applications such as active resource monitoring with support for deletions and machine unlearning. We show that all existing sketches for this model are vulnerable to adaptive adversarial attacks that apply even when the sketch size is polynomial in the length of the stream. To overcome these vulnerabilities, we present the first adaptively robust sketches for resettable streams that maintain polylogarithmic space complexity in the stream length. Our framework supports (sub) linear statistics including $L_p$ moments for $p\in[0,1]$ (in particular, Cardinality and Sum) and Bernstein statistics. We bypass strong impossibility results known for linear and composable sketches by designing dedicated streaming sketches robustified via Differential Privacy. Unlike standard robustification techniques, which provide limited benefits in this setting and still require polynomial space in the stream length, we leverage the Binary Tree Mechanism for continual observation to protect the sketch's internal randomness. This enables accurate prefix-max error guarantees with polylogarithmic space.

Problem

• resettable streaming
• adaptive adversarial attacks
• streaming sketches
• robustness
• differential privacy

Innovation

• adaptively robust
• resettable streaming
• differential privacy
• Binary Tree Mechanism
• polylogarithmic space