On the Robustness of CountSketch to Adaptive Inputs

The last decade saw impressive progress towards understanding the performance of algorithms in adaptive settings, where subsequent inputs may depend on the output from prior inputs. Adaptive settings arise in processes with feedback or with adversarial attacks. Existing designs of robust algorithms are generic wrappers of non-robust counterparts and leave open the possibility of better tailored designs. The lowers bounds (attacks) are similarly worst-case and their significance to practical setting is unclear. Aiming to understand these questions, we study the robustness of CountSketch, a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements. The sketch supports recovering l₂-heavy hitters of a vector (entries with (Eqaution presented)). We show that the classic estimator is not robust, and can be attacked with a number of queries of the order of the sketch size. We propose a robust estimator (for a slightly modified sketch) that allows for quadratic number of queries in the _sketch size, which is an improvement factor of √k (for k heavy hitters) over prior "blackbox" approaches.