arXiv:2405. 11454v3 Announce Type: replace Abstract: We study gradient testing and gradient estimation of smooth functions using only a comparison oracle that, given two points, indicates which one has the larger function value.
arXiv:2606. 27082v1 Announce Type: new Abstract: We study the problem of finding stationary points of non-convex functions when access to the objective is provided only through a comparison oracle that, given two points, outputs which has the larger function value.
arXiv:2601. 07326v4 Announce Type: replace-cross Abstract: This paper studies AdamW-style Shampoo, an effective variant of the classical Shampoo that won the external tuning track of the AlgoPerf neural network training competition.
arXiv:2605. 18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process.
arXiv:2607. 25492v2 Announce Type: replace Abstract: We study stochastic optimization with heavy-tailed gradient noise.
arXiv:2511. 11498v2 Announce Type: replace-cross Abstract: We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space.
arXiv:2310. 15976v4 Announce Type: replace Abstract: signSGD is attractive in nonconvex optimization because it communicates sign-valued rather than full-precision gradients.
arXiv:2410. 23212v3 Announce Type: replace-cross Abstract: In graph-based data analysis, $k$-nearest neighbor ($k$NN) graphs are widely used due to their adaptivity to local data densities.
arXiv:2509. 03734v3 Announce Type: replace-cross Abstract: In the hypothesis selection problem, we are given sample and query access to finite set of candidate distributions (hypotheses), $\mathcal{H} = \{H_1, \ldots, H_n\}$, and samples from an unknown distribution $P$, both over a domain $\mathcal{X}$.
arXiv:2605. 31152v2 Announce Type: replace-cross Abstract: This paper studies how efficiently deep ReLU neural networks can approximate and learn smooth functions.
arXiv:2606. 05438v1 Announce Type: new Abstract: We study the deterministic first-order oracle complexity of finding \(\epsilon\)-stationary points in smooth nonconvex optimization when the objective satisfies higher-order smoothness assumptions.
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
arXiv:2606. 14640v1 Announce Type: new Abstract: We study Online Convex Optimization (OCO) over a convex set $K\subseteq \mathbb R^d$, where in each round $t$ the learner selects $x_t\in K$ and then observes a convex loss $f_t:K\to[0,1]$, with the goal of minimizing regret to the best fixed decision in hindsight.