Adversarially Robust Streaming Algorithms via Differential Privacy

Hassidim, Avinatan; Kaplan, Haim; Mansour, Yishay; Matias, Yossi; Stemmer, Uri

doi:10.1145/3556972

Cited by 12 publications

(11 citation statements)

References 38 publications

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“…Kaplan et al [25] constructed a streaming problem naturally inspired by the adaptive data analysis literature, which exhibits a large separation between the space complexities in the adversarial and oblivious regimes. On the positive side, several recent works [4,23,48] present generic compilers that transform non-robust randomized streaming algorithms into efficient adversarially robust ones, for various classical problems such as distinct elements counting and 𝐹 𝑝 -sampling, among others. child of the 𝑖'th node, and otherwise 𝑦 𝑖 = 0.…”

Section: Streaming Algorithmsmentioning

confidence: 99%

Adversarial laws of large numbers and optimal regret in online classification

Alon

Ben‐Eliezer

Dagan

et al. 2021

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

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Laws of large numbers guarantee that given a large enough sample from some population, the measure of any fixed sub-population is well-estimated by its frequency in the sample. We study laws of large numbers in sampling processes that can affect the environment they are acting upon and interact with it. Specifically, we consider the sequential sampling model proposed by Ben-Eliezer and Yogev (2020), and characterize the classes which admit a uniform law of large numbers in this model: these are exactly the classes that are online learnable. Our characterization may be interpreted as an online analogue to the equivalence between learnability and uniform convergence in statistical (PAC) learning.The sample-complexity bounds we obtain are tight for many parameter regimes, and as an application, we determine the optimal regret bounds in online learning, stated in terms of Littlestone's dimension, thus resolving the main open question from Ben-David, Pál, and Shalev-Shwartz (2009), which was also posed by .

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Section: Streaming Algorithmsmentioning

confidence: 99%

Adversarial laws of large numbers and optimal regret in online classification

Alon

Ben‐Eliezer

Dagan

et al. 2021

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

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“…Our approach involves replacing hash functions in existing constructions with keyed PRFs, and so does involve cryptographic building blocks, but remains fully practical. Meanwhile, [25] considers adding robustness to streaming algorithms using differential privacy.…”

Section: Related Workmentioning

confidence: 99%

Adversarial Correctness and Privacy for Probabilistic Data Structures

Filić

Paterson

Unnikrishnan

et al. 2022

Proceedings of the 2022 ACM SIGSAC Conference on Computer and Communications Security

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We study the security of Probabilistic Data Structures (PDS) for handling Approximate Membership Queries (AMQ); prominent examples of AMQ-PDS are Bloom and Cuckoo filters. AMQ-PDS are increasingly being deployed in environments where adversaries can gain benefit from carefully selecting inputs, for example to increase the false positive rate of an AMQ-PDS. They are also being used in settings where the inputs are sensitive and should remain private in the face of adversaries who can access an AMQ-PDS through an API or who can learn its internal state by compromising the system running the AMQ-PDS.We develop simulation-based security definitions that speak to correctness and privacy of AMQ-PDS. Our definitions are general and apply to a broad range of adversarial settings. We use our definitions to analyse the behaviour of both Bloom filters and insertiononly Cuckoo filters. We show that these AMQ-PDS can be provably protected through replacement or composition of hash functions with keyed pseudorandom functions in their construction. We also examine the practical impact on storage size and computation of providing secure instances of Bloom and insertion-only Cuckoo filters.

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“…The adaptive setting, where inputs may depend on prior outputs, is more challenging to analyse and there is growing interest in quantifying performance and in designing methods that are robust to adaptive inputs. Works in this vein span machine learning [38,19,5,31], adaptive data analysis [17,25,28,22,16], dynamic graph algorithms [35,3,18,21,39,7], and sketching and streaming algorithms [29,3,23,9,24,41,6,8].…”

Section: Introductionmentioning

confidence: 99%

“…Robustness to adaptive inputs can trivially be achieved by using a fresh data structure for each query, or more finely, for each time the output changes, hence robustness guarantee that grows only linearly with sketch size. A powerful connection between adaptive robustness and differential privacy [16] and utilizing the workhorse of DP composition, yielded essentially a wrapper around ℓ non-robust independent replicas that supports a quadratic number Õ(ℓ 2 ) of adaptive queries (or changes to the output) [24,20,7]. Research works on robust streaming algorithms include [9,24,41,6,8,20,14].…”

Section: Introductionmentioning

confidence: 99%

“…A powerful connection between adaptive robustness and differential privacy [16] and utilizing the workhorse of DP composition, yielded essentially a wrapper around ℓ non-robust independent replicas that supports a quadratic number Õ(ℓ 2 ) of adaptive queries (or changes to the output) [24,20,7]. Research works on robust streaming algorithms include [9,24,41,6,8,20,14]. For the problem of recovering heavy-hitters from CountSketch, the "wrapper" method supports ≈ ǫℓ 2 adaptive queries.…”

Section: Introductionmentioning

confidence: 99%

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Tricking the Hashing Trick: A Tight Lower Bound on the Robustness of CountSketch to Adaptive Inputs

Cohen¹,

Nelson²,

Sarlós³

et al. 2022

Preprint

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CountSketch and Feature Hashing (the "hashing trick") are popular randomized dimensionality reduction methods that support recovery of ℓ2-heavy hitters (keys i where v 2 i > ǫ v 2 2 ) and approximate inner products. When the inputs are not adaptive (do not depend on prior outputs), classic estimators applied to a sketch of size O(ℓ/ǫ) are accurate for a number of queries that is exponential in ℓ. When inputs are adaptive, however, an adversarial input can be constructed after O(ℓ) queries with the classic estimator and the best known robust estimator only supports Õ(ℓ 2 ) queries. In this work we show that this quadratic dependence is in a sense inherent: We design an attack that after O(ℓ 2 ) queries produces an adversarial input vector whose sketch is highly biased. Our attack uses "natural" non-adaptive inputs (only the final adversarial input is chosen adaptively) and universally applies with any correct estimator, including one that is unknown to the attacker. In that, we expose inherent vulnerability of this fundamental method.

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Adversarially Robust Streaming Algorithms via Differential Privacy

Cited by 12 publications

References 38 publications

Adversarial laws of large numbers and optimal regret in online classification

Adversarial laws of large numbers and optimal regret in online classification

Adversarial Correctness and Privacy for Probabilistic Data Structures

Tricking the Hashing Trick: A Tight Lower Bound on the Robustness of CountSketch to Adaptive Inputs

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