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:2609. 08564v1 Announce Type: cross Abstract: We study distributed one-dimensional mean estimation under a 1-bit communication constraint.
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.
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.
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:2608. 06337v1 Announce Type: cross Abstract: A monotone adversary observes an i.
arXiv:2608. 06262v1 Announce Type: new Abstract: Model evaluations may fix all tests before observing any responses or select later tests using earlier responses.
Minimax risk and regret are expectation-based criteria and do not capture rare but consequential failures. To address this concern, we develop a $δ$-explicit minimax-quantile theory for interactive statistical decision making (ISDM).
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. 07922v1 Announce Type: new Abstract: Adaptive learning needs both a state that preserves what observations imply and opportunities to act on that state.
arXiv:2606. 25170v1 Announce Type: cross Abstract: We study PAC learning in tabular discounted Markov decision processes with exogenous i.