We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distribution over $\mathcal{X} \times \{0,1\}$, as in clas...
arXiv:2609.24260v1 Announce Type: cross Abstract: We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distrib...
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: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. 22889v1 Announce Type: new Abstract: Learning the natural parameters $z \in \mathbb{R}^n$ of discrete distributions $\mu_z$ from independent samples constrained to a subset $S \subseteq \{0,1\}^n$ is a foundational challenge in high-dimensional statistics.
arXiv:2608. 06825v1 Announce Type: new Abstract: Learning from correct demonstrations is harder than supervised learning when many answers are correct: after predicting, the learner sees one valid answer but not whether its own answer was valid, nor any reward.
arXiv:2608. 06363v1 Announce Type: cross Abstract: Let $H\subseteq\{-1,+1\}^X$ be a class of finite VC dimension $d\ge1$.
We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $Ω(n^2)$. By utilizing the special structure of these DNFs, we prove a lifting theorem with a constant-sized gadget that lifts the DNF to a communication problem, while losslessly translating the separation in certificate complexity to a separation in communication complexity.
arXiv:2608. 02533v1 Announce Type: cross Abstract: We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $\Omega(n^2)$.
arXiv:2608. 10869v1 Announce Type: new Abstract: Worst-case multiclass bounds do not become smaller when the best classifier is already nearly correct: what is missing is an optimistic rate, a guarantee whose fluctuation scales with the oracle risk itself.
arXiv:2608. 04686v1 Announce Type: new Abstract: We study distributionally robust PAC learning for the $0$--$1$-loss, where adversarial perturbations of the data distribution are constrained by a Cressie--Read divergence of order $k>1$ and radius $\rho\geq 0$.