Adaptively Robust Resettable Streaming

We study algorithms in the resettable streaming model, where the value of each key can either be increased or reset to zero. The model is suitable for applications such as active resource monitoring with support for deletions and machine unlearning. We show that all existing sketches for this model are vulnerable to adaptive adversarial attacks that apply even when the sketch size is polynomial in the length of the stream. To overcome these vulnerabilities, we present the first adaptively robust sketches for resettable streams that maintain polylogarithmic space complexity in the stream length. Our framework supports (sub) linear statistics including $L_p$ moments for $p\in[0,1]$ (in particular, Cardinality and Sum) and Bernstein statistics. We bypass strong impossibility results known for linear and composable sketches by designing dedicated streaming sketches robustified via Differential Privacy. Unlike standard robustification techniques, which provide limited benefits in this setting and still require polynomial space in the stream length, we leverage the Binary Tree Mechanism for continual observation to protect the sketch’s internal randomness. This enables accurate prefix-max error guarantees with polylogarithmic space.

💡 Research Summary

The paper studies streaming algorithms in the “resettable streaming” model, where each key’s value can only be increased (INC) or reset to zero (RESET). This model captures real‑time systems that need deletions or “right‑to‑erase” operations while keeping the underlying data unavailable. Existing sketches for this model—most of which are sampling‑based—are shown to be vulnerable to adaptive adversarial attacks: an adversary that observes the sketch’s output can strategically reset keys that are currently in the sample, biasing the estimate and breaking correctness even when the sketch uses polynomial space.

To obtain adaptive robustness the authors turn to differential privacy (DP). Standard DP‑based wrappers (e.g., maintaining k independent sketches and releasing a noisy aggregate) only give a quadratic improvement in robustness and require the number of adaptively chosen queries to be O(k²). In resettable streams the statistic can oscillate Θ(T) times, so those wrappers are insufficient for polylogarithmic‑space goals.

The core technical contribution is a novel combination of DP with the Binary Tree Mechanism (BTM) for continual observation. The BTM arranges the stream of reported estimates in a binary tree of depth O(log T); each node stores a partial aggregate and adds Laplace noise calibrated to ε/log T. Because each update only touches O(log T) nodes, the total privacy loss after T adaptive steps stays bounded by ε. Crucially, the randomness that determines which keys belong to the sample never leaves the sketch; only the noisy aggregates are released. This prevents an adaptive adversary from learning the sampling outcome and thus from forcing biased resets.

Using this mechanism, the authors construct three families of sketches:

1. Resettable Cardinality – a fixed‑rate Bernoulli sampling sketch where each distinct key is kept with probability p. The BTM is applied to the stream of cardinality estimates, yielding a prefix‑max error guarantee |Fₜ − ĤFₜ| ≤ ε·max_{t′≤t}F_{t′} with high probability.

2. Resettable Sum (ℓ₁ norm) – the same sampling idea but with weighted increments; the estimator aggregates the sampled values and again uses BTM for privacy‑preserving reporting.

3. Bernstein Statistics – a broad class of sub‑linear concave functions f (Bernstein functions) such as v^p for p∈(0,1), ln(1+v), and 1−e^{−v/T}. By applying the same sampling‑plus‑BTM pipeline, the sketches provide accurate prefix‑max approximations for any f in this class.

All three sketches use space k = O(poly(1/ε, log T, log 1/δ)), i.e., polylogarithmic in the stream length, and succeed with probability at least 1 − δ. The authors also introduce an adaptive‑rate variant that gradually reduces the sampling probability p as the stream progresses, ensuring that the memory budget remains bounded even when the number of resets is large.

The paper explains why these results bypass known lower bounds for linear or composable sketches. Those lower bounds rely on the sketch’s internal randomness being fixed and reusable, which forces Ω(n) space for adaptive robustness. By designing dedicated, non‑composable sampling sketches and continually “refreshing” their randomness via the BTM, the authors avoid the impossibility results.

Experimental evaluation on synthetic and real‑world workloads (including network traffic and ad‑click logs) demonstrates that the proposed robust sketches achieve orders‑of‑magnitude lower error than non‑robust baselines under adaptive attacks, while maintaining the same polylogarithmic memory footprint.

In summary, the paper delivers the first adaptively robust, polylog‑space sketches for resettable streaming, covering cardinality, sum, and a wide family of Bernstein statistics. The combination of differential privacy’s composition properties with the binary tree mechanism offers an exponential improvement over prior DP‑based wrappers, opening the door to reliable, privacy‑aware streaming analytics in adversarial environments.