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: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:2607. 02896v1 Announce Type: cross Abstract: We ask whether interaction is necessary for order-optimal 1-bit mean estimation over nonparametric finite-moment classes.
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. 09668v1 Announce Type: new Abstract: Contextual queueing bandits provide a framework for learning to schedule heterogeneous jobs under unknown context-dependent service rates.
arXiv:2609. 27860v1 Announce Type: new Abstract: A pointwise-unbiased one-bit compressor reconstructs every real input in expectation while transmitting one bit.
arXiv:2606. 25170v1 Announce Type: cross Abstract: We study PAC learning in tabular discounted Markov decision processes with exogenous i.
arXiv:2608. 06337v1 Announce Type: cross Abstract: A monotone adversary observes an i.
arXiv:2606. 14690v1 Announce Type: new Abstract: We study a \emph{max-risk} objective for active learning in a multi-group mean estimation $d$-armed bandits: a learner adaptively allocates a budget of $T$ samples across $d$ groups to minimize the worst-case uncertainty index $\max_{k\in[d]}\sigma_k^2/n_k$, where $\sigma_k$ is the standard deviation of the distribution of arm $d$, and $n_k$ is the number of times arm $d$ is sampled.
arXiv:2609. 20687v1 Announce Type: cross Abstract: We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p < q$) can improve convergence rates in convex optimization, and matching prior lower bounds up to logarithmic factors.
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.