A Framework for Adversarially Robust Streaming Algorithms

Ben‐Eliezer, Omri; Jayaram, Rajesh; Woodruff, David P.; Yogev, Eylon

doi:10.1145/3375395.3387658

Cited by 29 publications

(22 citation statements)

References 31 publications

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“…In this paper, we design streaming algorithms in the adversarially robust streaming model of Ben-Eliezer et al [BEJWY20], which we now introduce in the context of computing a (1 ± α)approximation to values of a function f . Definition 5 (Adversarially robust streaming).…”

Section: Adversarially Robust Streaming Algorithmsmentioning

confidence: 99%

“…The flip number, defined in [BEJWY20], plays a prominent role in many of the previous results on adversarially robust streaming. For completeness, we next provide its definition suited for our context.…”

Section: Flip Numbermentioning

confidence: 99%

“…There is already a wide range of problems and settings for which the best known adversarially robust streaming algorithms are almost as efficient as their classical, non-robust counterparts. The flip number [BEJWY20] of a streaming problem, an algorithmic stability parameter which counts how many times the output value may change by a multiplicative factor of 1 + α as the stream progresses, plays a central role in many of these results [HKM + 20, WZ20, KMNS21, ACSS21]. When the flip number λ is small, the generic methods developed in these works can turn a classical streaming algorithm into an adversarially robust one with only a small overhead (linear in λ or better) in the space complexity.…”

Section: Introductionmentioning

confidence: 99%

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Adversarially Robust Streaming via Dense--Sparse Trade-offs

Ben‐Eliezer¹,

Eden²,

Onak³

2021

Preprint

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A streaming algorithm is adversarially robust if it is guaranteed to perform correctly even in the presence of an adaptive adversary. The development and analysis of such algorithms have been a very active topic recently, and several sophisticated frameworks for robustification of classical streaming algorithms have been developed. One of the main open questions in this area is whether efficient adversarially robust algorithms exist for moment estimation problems (e.g., F 2 -estimation) under the turnstile streaming model, where both insertions and deletions are allowed. So far, the best known space complexity for streams of length m, achieved using differential privacy (DP) based techniques, is of order Õ(m 1/2 ) for computing a constant-factor approximation with high constant probability (the Õ notation hides here terms polynomial in log m and log n, where n is the universe size). In this work, we propose a new simple approach to tracking moments by alternating between two different regimes: a sparse regime, in which we can explicitly maintain the current frequency vector and use standard sparse recovery techniques, and a dense regime, in which we make use of existing DP-based robustification frameworks. The results obtained using our technique break the previous m 1/2 barrier for any fixed p. More specifically, our space complexity for F 2 -estimation is Õ(m 2/5 ) and for F 0estimation, i.e., counting the number of distinct elements, it is Õ(m 1/3 ).All existing robustness frameworks have their space complexity depend multiplicatively on a parameter λ called the flip number of the streaming problem, where λ = m in turnstile moment estimation. The best known dependence in these frameworks (for constant factor approximation) is of order Õ(λ 1/2 ), and it is known to be tight for certain problems. Again, our approach breaks this barrier, achieving a dependence of order Õ(λ 1/2−c(p) ) for F p -estimation, where c(p) > 0 depends only on p.

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Section: Adversarially Robust Streaming Algorithmsmentioning

confidence: 99%

Section: Flip Numbermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adversarially Robust Streaming via Dense--Sparse Trade-offs

Ben‐Eliezer¹,

Eden²,

Onak³

2021

Preprint

Self Cite

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“…The adversarial streaming model, in various forms, was considered by [MNS11, GHR + 12, GHS + 12, AGM12a,AGM12b,HW13,BY19,BJWY20,HKM + 20,KMNS21,BHM + 21]. We give here the formulation presented by Ben-Eliezer et al [BJWY20]. The adversarial setting is modeled by a two-player game between a (randomized) StreamingAlgorithm and an Adversary.…”

Section: The Adversarial Streaming Modelmentioning

confidence: 99%

“…To illustrate the results of [BJWY20], let us consider the distinct elements problem, in which the function F counts the number of distinct elements in the stream. Observe that, assuming that there are no deletions in the stream, this quantity is monotonically increasing.…”

Section: Existing Framework: Ben-eliezer Et Al [Bjwy20]mentioning

confidence: 99%

A Framework for Adversarial Streaming via Differential Privacy and Difference Estimators

Idan¹,

Cohen²,

Shechner³

et al. 2021

Preprint

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Streaming algorithms are algorithms for processing large data streams, using only a limited amount of memory. Classical streaming algorithms operate under the assumption that the input stream is fixed in advance. Recently, there is a growing interest in studying streaming algorithms that provide provable guarantees even when the input stream is chosen by an adaptive adversary. Such streaming algorithms are said to be adversarially-robust. We propose a novel framework for adversarial streaming that hybrids two recently suggested frameworks by Hassidim et al. (2020) and by Woodruff and Zhou (2021). These recently suggested frameworks rely on very different ideas, each with its own strengths and weaknesses. We combine these two frameworks (in a nontrivial way) into a single hybrid framework that gains from both approaches to obtain superior performances for turnstile streams.

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Robust Property-Preserving Hash Functions for Hamming Distance and More

Fleischhacker

Simkin

2021

Lecture Notes in Computer Science

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A Framework for Adversarially Robust Streaming Algorithms

Cited by 29 publications

References 31 publications

Adversarially Robust Streaming via Dense--Sparse Trade-offs

Adversarially Robust Streaming via Dense--Sparse Trade-offs

A Framework for Adversarial Streaming via Differential Privacy and Difference Estimators

Robust Property-Preserving Hash Functions for Hamming Distance and More

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