Adaptively Robust Resettable Streaming

TL;DR

This paper introduces the first adaptively robust streaming sketches for resettable streams, using differential privacy and the Binary Tree Mechanism to achieve polylogarithmic space complexity and withstand adaptive adversarial attacks.

Contribution

It develops a novel framework for robust streaming algorithms in resettable models, overcoming previous vulnerabilities and strong impossibility results.

Findings

Supports linear and nonlinear statistics like $L_p$ moments and Bernstein statistics.

Achieves polylogarithmic space complexity in the stream length.

Provides accurate prefix-max error guarantees.

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.