arXiv:2608. 02538v1 Announce Type: cross Abstract: This paper is concerned with one-bit mean estimation, where each independent sample is represented by a single binary message.
arXiv:2609. 08564v1 Announce Type: cross Abstract: We study distributed one-dimensional mean estimation under a 1-bit communication constraint.
We study distributed one-dimensional mean estimation under a 1-bit communication constraint. Each agent observes one sample, drawn independently from an unknown distribution, and returns a single bit in response to a query $Q: \mathbb{R}\to\{0,1\}$ chosen by a central learner.
arXiv:2607. 02896v1 Announce Type: cross Abstract: We ask whether interaction is necessary for order-optimal 1-bit mean estimation over nonparametric finite-moment classes.
arXiv:2607. 16966v1 Announce Type: cross Abstract: Estimating entropy from samples is fundamental in information theory and property testing.
arXiv:2606. 00703v1 Announce Type: cross Abstract: Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible.
arXiv:2608. 06262v1 Announce Type: new Abstract: Model evaluations may fix all tests before observing any responses or select later tests using earlier responses.
arXiv:2610.01951v1 Announce Type: cross Abstract: Top-two algorithms are simple and effective for fixed-confidence best-arm identification, but their sharp non-asymptotic behavior is still not well u...
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.
arXiv:2609. 27860v1 Announce Type: new Abstract: A pointwise-unbiased one-bit compressor reconstructs every real input in expectation while transmitting one bit.
arXiv:2609.13703v1 Announce Type: cross Abstract: In the best-arm identification problem, we are given $n$ stochastic arms with unknown means and wish to identify the arm with the largest mean with p...
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:2606. 25170v1 Announce Type: cross Abstract: We study PAC learning in tabular discounted Markov decision processes with exogenous i.