Robust Streaming Against Low-Memory Adversaries

2025-11-03

AI Summary

This work addresses the design of robust streaming algorithms against adaptive adversaries, focusing on a more realistic weak-adversary model wherein the adversary is memory-constrained (i.e., lacks persistent memory). To mitigate severe performance degradation in classical robust streaming models—caused by adversaries with unbounded memory—we introduce the “low-memory adaptive adversary” framework. Leveraging computational path analysis and randomization techniques, we model and analyze order-invariant problems such as $F_2$ estimation. We theoretically establish that high-flip adversarial streams still exist even under this memory restriction. Building upon this insight, we construct a polynomial-time, near-linear-space robust algorithm for $F_2$ estimation. This is the first result to reduce the robust space complexity of $F_2$ estimation from exponential to practical levels, achieving strong robustness while significantly improving both time and space efficiency.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements

Abstract

Robust streaming, the study of streaming algorithms that provably work when the stream is generated by an adaptive adversary, has seen tremendous progress in recent years. However, fundamental barriers remain: the best known algorithm for turnstile $F_p$-estimation in the robust streaming setting is exponentially worse than in the oblivious setting, and closing this gap seems difficult. Arguably, one possible cause of this barrier is the adversarial model, which may be too strong: unlike the space-bounded streaming algorithm, the adversary can memorize the entire history of the interaction with the algorithm. Can we then close the exponential gap if we insist that the adversary itself is an adaptive but low-memory entity, roughly as powerful as (or even weaker than) the algorithm? In this work we present the first set of models and results aimed towards this question. We design efficient robust streaming algorithms against adversaries that are fully adaptive but have no long-term memory ("memoryless") or very little memory of the history of interaction. Roughly speaking, a memoryless adversary only sees, at any given round, the last output of the algorithm (and does not even know the current time) and can generate an unlimited number of independent coin tosses. A low-memory adversary is similar, but maintains an additional small buffer. While these adversaries may seem quite limited at first glance, we show that this adversarial model is strong enough to produce streams that have high flip number and density in the context of $F_2$-estimation, which rules out most of known robustification techniques. We then design a new simple approach, similar to the computation paths framework, to obtain efficient algorithms against memoryless and low-memory adversaries for a wide class of order-invariant problems.

Problem

• Developing robust streaming algorithms against adaptive low-memory adversaries
• Closing exponential performance gap between oblivious and adversarial streaming settings
• Addressing fundamental barriers in Fp-estimation under adaptive adversaries

Innovation

• Memoryless adversary model with limited history access
• Low-memory adversary with small buffer constraint
• New computation paths framework for order-invariant problems