The note provides a detailed proof of Astra’s lower bound for differentially private continual counting, building on recent work by Harrison and Leeman. It discusses earlier results, including a Ω(√{3}√{log(n)}) bound by Bairaktari and Larsen and their subsequent Ω(log^2(n)) bound for pure differential privacy. The authors aim to offer a more natural and accessible proof, hoping to aid further research in the area.
arXiv:2607. 00876v3 Announce Type: replace-cross Abstract: Private continual counting is a fundamental problem in differential privacy: given a binary stream of length $n$, where each $1$ corresponds to the contribution of one individual, the goal is to release all running counts while protecting the privacy of each individual.
arXiv:2607. 00876v1 Announce Type: cross Abstract: Private continual counting is a fundamental problem in differential privacy: given a binary stream of length $n$, where each $1$ corresponds to the contribution of one individual, the goal is to release all running counts while protecting the privacy of each individual.
arXiv:2511. 13999v2 Announce Type: replace Abstract: We study the running time, in terms of first order oracle queries, of differentially private empirical/population risk minimization of Lipschitz convex losses.
arXiv:2602. 01607v3 Announce Type: replace-cross Abstract: Differentially private synthetic data enables the sharing and analysis of sensitive datasets while providing rigorous privacy guarantees for individual contributors.
arXiv:2406. 13668v4 Announce Type: replace Abstract: A set of probabilistic forecasts is calibrated if each prediction of the forecaster closely approximates the empirical distribution of outcomes on the subset of timesteps where that prediction was made.
arXiv:2604. 10819v2 Announce Type: replace-cross Abstract: A recent line of work initiated by Chiesa and Gur and further developed by Herman and Rothblum investigates the sample and communication complexity of verifying properties of distributions with the assistance of a powerful, knowledgeable, but untrusted prover.
The paper investigates the limits of accelerating gradient descent (GD) using predetermined step sizes in smooth convex optimization. It establishes new lower bounds: an ≥·n−1.6342 non‑anytime bound and an ≥·n−1.2408 anytime bound, surpassing previous results. These findings also demonstrate a strict separation between convergence exponents achievable in non‑anytime versus anytime settings.
The paper establishes the optimal incremental first‑order oracle (IFO) complexity for nonconvex finite‑sum optimization under individual smoothness, proving a matching lower bound that closes a previously missing √{n} factor. It also refines the analysis of the PAGE algorithm under the global Polyak‑Lojasiewicz condition, providing tighter guarantees for different ranges of the condition number. The authors introduce a novel dense weak hiding construction that yields these lower bounds and demonstrates the limits of existing methods.
The paper revisits realizable multiclass PAC learning with bandit feedback, correcting a previously claimed lower bound on sample complexity. It introduces a new anchored dimension, “aBDS,” and establishes a constant‑free three‑part lower bound, while also providing tighter upper bounds that eliminate dependence on the total label count. The authors demonstrate that the optimal sample complexity can vary dramatically even among classes with identical dimensional profiles, revealing a confidence direct‑sum phenomenon and a rank‑saturation phase transition.
arXiv:2609. 29696v1 Announce Type: new Abstract: We construct, for every function class $\mathcal{F}\subseteq[0,1]^{\mathcal{X}}$ and every accuracy $0<\alpha\le 1$, an agnostic sample compression scheme for the empirical squared loss: for every finite sample $S\in(\mathcal{X}\times[0,1])^m$ with arbitrary (noisy) labels, the scheme stores at most $O(\mathrm{fat}(\mathcal{F},c'\alpha)\cdot\log^3(2/\alpha))$ original labeled examples and auxiliary bits, independent of the sample size $m$, and reconstructs a function $\hat f$ with $L_2(\hat f,S)\le\inf_{f\in\mathcal{F}}L_2(f,S)+\alpha$.
arXiv:2607. 16966v1 Announce Type: cross Abstract: Estimating entropy from samples is fundamental in information theory and property testing.
arXiv:2609.09152v1 Announce Type: cross Abstract: We study how far gradient descent (GD) can be accelerated by predetermined nonnegative stepsizes in smooth convex optimization. Writing $p_{\mathrm{s...