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.

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对抗性鲁棒流算法的框架

我们研究了流式算法的对抗鲁棒性。在这种情况下，如果一个算法的性能保证成立，即使该流是由沿着流观察算法的输出并且可以以在线方式做出反应的对手自适应地选择的，则该算法被认为是稳健的。虽然确定性流算法本质上是健壮的，但流文献中的许多核心问题并不承认亚线性空间确定性算法。另一方面，针对这些问题的经典空间高效随机算法通常不具有对抗性鲁棒性。这就提出了一个自然的问题，即是否存在针对这些问题的有效的对抗性鲁棒（随机）流算法。