In the adversarial streaming model, the input is a sequence of adaptive updates that defines an underlying dataset and the goal is to approximate, collect, or compute some statistic while using space sublinear in the size of the dataset. In 2022, Ben-Eliezer, Eden, and Onak showed a dense-sparse trade-off technique that elegantly combined sparse recovery with known techniques using differential privacy and sketch switching to achieve adversarially robust algorithms for $L_p$ estimation and other algorithms on turnstile streams. In this work, we first give an improved algorithm for adversarially robust $L_p$-heavy hitters, utilizing deterministic turnstile heavy-hitter algorithms with better tradeoffs. We then utilize our heavy-hitter algorithm to reduce the problem to estimating the frequency moment of the tail vector. We give a new algorithm for this problem in the classical streaming setting, which achieves additive error and uses space independent in the size of the tail. We then leverage these ingredients to give an improved algorithm for adversarially robust $L_p$ estimation on turnstile streams.

翻译：在对抗性流模型中，输入是一系列自适应更新，这些更新定义了一个底层数据集，目标是在使用空间小于数据集大小的条件下，近似、收集或计算某些统计量。2022年，Ben-Eliezer、Eden和Onak提出了一种稠密-稀疏权衡技术，该技术巧妙地将稀疏恢复与差分隐私和草图切换等已知技术相结合，实现了旋转门流上$L_p$估计及其他算法的对抗鲁棒性算法。在本工作中，我们首先提出了一种改进的对抗鲁棒$L_p$-heavy hitters算法，该算法利用具有更好权衡特性的确定性旋转门heavy-hitter算法。随后，我们利用该heavy-hitter算法将问题简化为估计尾部向量的频率矩。我们针对经典流设置下的该问题提出了一种新算法，该算法实现了加性误差，且所用空间与尾部大小无关。最后，我们整合这些技术要素，提出了一种改进的旋转门流上对抗鲁棒$L_p$估计算法。