arXiv:2608.30254v1 Announce Type: new Abstract: We resolve the threshold part of Question 4 of the COLT 2025 open problem "Data Selection for Regression Tasks" of Hanneke, Moran, Shlimovich and Yehud...
arXiv:2608. 28007v1 Announce Type: new Abstract: Hanneke, Moran, Shlimovich and Yehudayoff (COLT 2025) posed the following open problem.
arXiv:2608. 15472v1 Announce Type: cross Abstract: The problem of networked information aggregation, studied in Kearns et al.
Bakhtiari, Lattimore and Szepesvári (COLT 2025) proved that Thompson sampling (TS) has Bayesian regret $\tilde O(d^{5/2}\sqrt n)$ for bandit convex optimisation with convex \emph{monotone} ridge losse...
arXiv:2607. 18652v3 Announce Type: replace-cross Abstract: We establish improved lower bounds on the minimax expected regret of stochastic bandit convex optimization for $1$-Lipschitz functions on the $d$-dimensional Euclidean ball.
The paper investigates the geometry of full conformal prediction (FullCP) regions produced by an empirical energy‑form pairwise score. It shows that convexity of the candidate score alone does not ensure connected FullCP regions, and establishes conditions under which comparison regions share a common minimizer, making the exact conformal region star‑shaped. For power distances with exponent β≥1 the geometry is deterministic, and for β between 1 and 2 explicit Lipschitz bounds allow certified inner and outer radial envelopes with Hausdorff guarantees.
arXiv:2609. 03762v1 Announce Type: new Abstract: The computation of the Bures-Wasserstein (BW) barycenter of an ensemble of positive definite matrices arises throughout machine learning, optimal transport, and quantum information.
arXiv:2608. 08399v1 Announce Type: new Abstract: The instance-wise $F_1$ measure is a central performance measure for multi-label classification.
arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.
We establish a $\widetildeΩ(d^{5/4}\sqrt T)$ lower bound on the minimax expected regret of stochastic bandit convex optimization of $1$-Lipschitz functions on the Euclidean ball. This presents the first nontrivial regret lower bound that grows faster than $d\sqrt{T}$ for this problem, establishing that stochastic bandit convex optimization is fundamentally harder than linear bandits.
Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a smaller problem. Standard subspace embeddings guarantee that the cost of the regress...
The paper introduces a Projected Riemannian Gradient Descent (RGD) algorithm for computing the Bures‑Wasserstein barycenter of positive definite matrices, achieving dimension‑independent linear convergence at unit step size. It resolves a previous dichotomy by showing that clipping eigenvalues to a fixed interval yields a closed‑form, non‑expansive projection in the BW metric, allowing the algorithm to match the empirical speed of unit‑step RGD while maintaining theoretical guarantees. The method also extends to the invariant matrix projection problem, providing a unified dimension‑independent analysis.