A Framework for Adversarially Robust Streaming Algorithms

03/31/2020
by   Omri Ben-Eliezer, et al.
0

We investigate the adversarial robustness of streaming algorithms. In this context, an algorithm is considered robust if its performance guarantees hold even if the stream is chosen adaptively by an adversary that observes the outputs of the algorithm along the stream and can react in an online manner. While deterministic streaming algorithms are inherently robust, many central problems in the streaming literature do not admit sublinear-space deterministic algorithms; on the other hand, classical space-efficient randomized algorithms for these problems are generally not adversarially robust. This raises the natural question of whether there exist efficient adversarially robust (randomized) streaming algorithms for these problems. In this work, we show that the answer is positive for various important streaming problems in the insertion-only model, including distinct elements and more generally F_p-estimation, F_p-heavy hitters, entropy estimation, and others. For all of these problems, we develop adversarially robust (1+ε)-approximation algorithms whose required space matches that of the best known non-robust algorithms up to a poly(log n, 1/ε) multiplicative factor (and in some cases even up to a constant factor). Towards this end, we develop several generic tools allowing one to efficiently transform a non-robust streaming algorithm into a robust one in various scenarios.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

01/26/2021

Separating Adaptive Streaming from Oblivious Streaming

We present a streaming problem for which every adversarially-robust stre...
09/08/2021

Adversarially Robust Streaming via Dense–Sparse Trade-offs

A streaming algorithm is adversarially robust if it is guaranteed to per...
06/26/2019

The Adversarial Robustness of Sampling

Random sampling is a fundamental primitive in modern algorithms, statist...
07/12/2020

Streaming Algorithms for Online Selection Problems

The model of streaming algorithms is motivated by the increasingly commo...
07/30/2021

A Framework for Adversarial Streaming via Differential Privacy and Difference Estimators

Streaming algorithms are algorithms for processing large data streams, u...
10/07/2020

New Verification Schemes for Frequency-Based Functions on Data Streams

We study the general problem of computing frequency-based functions, i.e...
11/26/2019

Pseudo-deterministic Streaming

A pseudo-deterministic algorithm is a (randomized) algorithm which, when...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.