arXiv:2510. 01878v2 Announce Type: replace Abstract: Low-rank gradient optimization for large language models is currently divided into two categories: structured methods that rigorously identify subspaces, and randomized approaches employed primarily for computational efficiency.
arXiv:2606. 00413v1 Announce Type: cross Abstract: Sufficient dimension reduction (SDR) makes high-dimensional regression tractable by projecting the covariates onto a low-dimensional subspace that preserves the conditional mean of the response.
arXiv:2609.15723v1 Announce Type: new Abstract: Traditional variance reduction methods (e.g., SPIDER, SARAH, STORM) have been extensively investigated for improving the convergence rates of stochasti...
arXiv:2604. 24012v3 Announce Type: replace Abstract: Federated learning enables a population of clients to collaboratively train machine learning models without exchanging their raw data, but standard algorithms such as FedAvg suffer from slow convergence and high communication and memory costs in heterogeneous, resource-constrained environments.
arXiv:2606. 15832v1 Announce Type: new Abstract: Empirical risk minimization on massive datasets naturally exhibits a nested double finite-sum structure, where $N=nm$ total samples are logically or physically partitioned into $n$ blocks of size $m$ (e.
arXiv:2508. 00775v2 Announce Type: replace-cross Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems.
arXiv:2609.08277v1 Announce Type: new Abstract: We study zeroth-order optimization of non-convex functions with the aid of directional hints, which are cheap but potentially inaccurate approximations...
The paper introduces Batched SGD, a variant that groups online samples into epochs and performs a single update per epoch using a low‑variance gradient estimate. This batching approach allows a straightforward high‑probability analysis without restrictive assumptions or auxiliary sequences, yielding near‑optimal rates for both strongly convex and non‑convex objectives under standard smoothness and sub‑Gaussian noise conditions. The authors also extend the method to federated learning, providing the first high‑probability guarantees with logarithmic communication complexity, linear speedup in the number of agents, and robustness to data heterogeneity.
arXiv:2607. 15412v1 Announce Type: new Abstract: Multi-objective learning (MOL) aims to optimize multiple objectives simultaneously.
arXiv:2607. 16261v1 Announce Type: cross Abstract: Modern optimizers combine gradients from the current mini-batch with historical optimization state, such as momentum or adaptive moments.
arXiv:2608. 12009v1 Announce Type: cross Abstract: Bregman proximal stochastic gradient (BPSG) methods bring variance-reduced composite optimization to objectives whose geometry is poorly captured by Euclidean smoothness.
The paper introduces a learning-based surrogate approach for stochastic optimization problems where uncertainty depends on the decision, modeled via a nonparametric regression. It constructs a surrogate that embeds iteratively updated Jacobian estimates, using an adaptive random design that focuses sampling near the current iterate to achieve dimension‑independent convergence of the Jacobian estimates. The resulting learning‑based stochastic prox‑linear (L‑SPL) algorithm demonstrates nonasymptotic convergence rates and outperforms existing methods in sample efficiency and objective value in numerical experiments.