The paper introduces RanSOM, a second‑order momentum algorithm that eliminates the need for a Lipschitz Hessian or auxiliary forward/backward passes by randomizing the step length. By sampling the step from an exponential distribution and using a Stein‑type identity, the method obtains an unbiased estimate of the gradient change with a single Hessian‑vector product that also serves the next gradient computation. RanSOM-E achieves optimal oracle‑complexity exponents for heavy‑tailed noise without clipping, while RanSOM-B preserves feasibility for Frank‑Wolfe iterates, and experiments on CIFAR‑10 show comparable accuracy to existing methods with lower update time.
arXiv:2610. 13789v1 Announce Type: new Abstract: Momentum methods such as STORM and second-order momentum track the gradient by adding a transport correction to momentum, at the cost of an extra oracle call per iteration.
arXiv:2310. 15976v4 Announce Type: replace Abstract: signSGD is attractive in nonconvex optimization because it communicates sign-valued rather than full-precision gradients.
arXiv:2610. 33381v2 Announce Type: new Abstract: Training is often stopped at a data-dependent time, so guarantees for the last iterate must hold at all times simultaneously.
arXiv:2609. 04578v1 Announce Type: cross Abstract: We study stochastic gradient descent with random reshuffling for finite sums \[ F(x)=\frac1n\sum_{i=1}^n f_i(x).
arXiv:2609. 21880v1 Announce Type: cross Abstract: We study the optimization of convex objectives with $(L,\kappa-1)$-H\"older-continuous gradients in $\ell_q$ over $R B_p^d$, $1<\kappa\le 2$.
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:2609.30499v1 Announce Type: new Abstract: Uniform noise-moment bounds exclude stochastic gradients whose variability increases with the iterate. We study ordinary, single-sample stochastic grad...
arXiv:2609.39595v1 Announce Type: new Abstract: Practical Muon maintains momentum and performs a small, fixed number of Newton--Schulz iterations separately for each parameter matrix, often with a Ne...
The paper studies contextual bilateral trade with full feedback, showing that action-independent observations eliminate the usual polynomial adaptation penalty seen in heavy-tailed bandits. It presents fully parameter-free algorithms that achieve oracle minimax regret rates without knowing the moment order or scale, and derives new regret bounds for both parametric and nonparametric settings. The key technical insight is a paired squared‑loss statistic whose noise cancels, enabling model selection and yielding regret rates that interpolate between classical nonparametric and linear extremes.
arXiv:2602. 05657v2 Announce Type: replace Abstract: The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm.
arXiv:2504.09409v3 Announce Type: replace-cross Abstract: In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems with exact constraints and stochastic objective e...
In this work, we study the oracle complexity of finding an $ε$-stationary point for nonconvex-strongly-convex (NC-SC) bilevel optimization using only first-order oracles. Existing methods achieving th...