[Paper Review] A Framework for Adversarial Streaming via Differential Privacy and Difference Estimators

Idan Attias, Edith Cohen+2 more|arXiv (Cornell University)|Jul 30, 2021

Privacy-Preserving Technologies in Data5 citations

TL;DR

This paper presents a hybrid framework that combines differential privacy and difference estimators to build adversarially robust streaming algorithms, achieving optimal space complexity for functions with bounded flip and twist numbers. The framework enables (1±α)-accurate tracking of F2 in turnstile streams with space complexity Õ(√(αλ + μ)/α² · log³·⁵m), resolving an open question on combining prior adversarial streaming approaches.

ABSTRACT

Classical streaming algorithms operate under the (not always reasonable) assumption that the input stream is fixed in advance. Recently, there is a growing interest in designing robust streaming algorithms that provide provable guarantees even when the input stream is chosen adaptively as the execution progresses. We propose a new framework for robust streaming that combines techniques from two recently suggested frameworks by Hassidim et al. [NeurIPS 2020] and by Woodruff and Zhou [FOCS 2021]. These recently suggested frameworks rely on very different ideas, each with its own strengths and weaknesses. We combine these two frameworks into a single hybrid framework that obtains the "best of both worlds", thereby solving a question left open by Woodruff and Zhou.

Motivation & Objective

• To address the limitations of existing adversarial streaming frameworks that rely on either differential privacy or difference estimators alone.
• To unify two complementary approaches—Hassidim et al. (NeurIPS 2020) and Woodruff & Zhou (FOCS 2021)—into a single robust framework.
• To achieve optimal space complexity for functions with bounded flip and twist numbers, particularly for F2 in the turnstile model.
• To resolve an open problem posed by Woodruff and Zhou regarding the combination of these two frameworks.

Proposed method

• The framework integrates a difference estimator (DE) and a tracker (TDE) to estimate function values under adversarial input.
• It uses a Guardian module that maintains multiple strong trackers (EM estimators) to ensure robustness against adversarial input sequences.
• A calibrated thresholding mechanism prevents overfitting by capping updates based on estimated flip and twist numbers.
• The framework leverages differential privacy to ensure stability under adaptive stream updates.
• It combines space-efficient difference estimators with strong tracking to maintain accuracy under adversarial conditions.
• Theoretical analysis ensures (1±α)-accuracy with high probability, using polylogarithmic overhead in key parameters.

Experimental results

Research questions

• RQ1 Can a unified framework be designed that combines the strengths of differential privacy and difference estimators for adversarial streaming?
• RQ2 What is the optimal space complexity for adversarially robust F2 estimation in the turnstile model?
• RQ3 How can flip and twist numbers be used to bound the space complexity of robust streaming algorithms?
• RQ4 Can the framework be extended to handle functions with high flip or twist numbers without incurring excessive space cost?
• RQ5 Does the hybrid approach outperform existing frameworks in terms of space efficiency and accuracy guarantees?

Key findings

• The framework achieves (1±α)-accurate F2 estimation in turnstile streams with space complexity Õ(√(αλ + μ)/α² · log³·⁵m), where λ is the (α′,m)-flip number and μ is the (γ₀,m)-twist number.
• The space complexity is optimal up to polylogarithmic factors, subsuming both the differential privacy and difference estimator frameworks.
• The framework resolves an open problem by Woodruff and Zhou, providing a unified solution that combines the best aspects of both prior approaches.
• The Guardian module ensures α-accuracy with high probability (1−1/m) by maintaining KM strong trackers with calibrated thresholds.
• Theoretical analysis confirms that the framework maintains robustness under adaptive stream updates, even when the adversary observes all previous outputs.
• The framework is general and applicable to any function with bounded flip and twist numbers, extending beyond F2 to other streaming functions.