The paper investigates sparse data augmentation for nonconvex optimization in geometric machine learning. It shows that using a small, fixed sample of transformations—obtained before optimization—allows gradient descent to achieve an ε‑stationary point of the fully augmented objective with ≤ O((log|G|+log(1/δ))/ε²) transformation queries. This is more efficient than both full augmentation and standard group‑SGD, which require O(1/ε⁴) queries.
arXiv:2609.08133v1 Announce Type: cross Abstract: In nonconvex optimization problems arising in geometric machine learning, data augmentation is commonly used to promote invariance by averaging empir...
arXiv:2606. 24418v1 Announce Type: new Abstract: Data augmentation is a simple and model-agnostic approach for exploiting known invariances in learning problems.
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: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...
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:2601. 18115v2 Announce Type: replace Abstract: We study the problem of learning a single neuron under standard squared loss in the presence of arbitrary label noise and group-level distributional shifts, for a broad family of covariate distributions.
arXiv:2511. 13592v2 Announce Type: replace-cross Abstract: The existing method of GS-PowerOpt solves the non-convex optimization problem of the form $\max_{\boldsymbol{x} \in \mathbb{R}^d} f(\boldsymbol{x})$ through maximizing a Gaussian-smoothed surrogate $F_{N,\sigma}(\boldsymbol{\mu}) = \mathbb{E}_{\boldsymbol{x}\sim\mathcal{N}(\boldsymbol{\mu},\sigma^2 I_d)}[e^{N f(\boldsymbol{x})}]$.
arXiv:2310. 15976v4 Announce Type: replace Abstract: signSGD is attractive in nonconvex optimization because it communicates sign-valued rather than full-precision gradients.
The paper studies algorithms for computing the Entropic Gromov-Wasserstein (EGW) distance, a measure of discrepancy between metric measure spaces. It introduces Averaged Mirror Descent (AMD), which averages successive Mirror Descent steps and is proven to converge for any cost function, and shows that a dual gradient method with a fixed step size also converges for arbitrary costs, even when iterations are inexact. Empirical comparisons demonstrate that both AMD and the dual gradient method succeed on cases where classical Mirror Descent fails.
arXiv:2505.20817v3 Announce Type: replace-cross Abstract: Gradient clipping is widely used in language-model training to control heavy-tailed gradient noise and can improve convergence guarantees ove...
arXiv:2602. 02877v2 Announce Type: replace Abstract: This paper studies optimization for a family of problems termed $\textbf{compositional entropic risk minimization}$, in which each data's loss is formulated as a Log-Expectation-Exponential (Log-E-Exp) function.
arXiv:2605. 28335v2 Announce Type: replace Abstract: Federated Learning (FL) enables multiple clients to collaboratively train models without sharing raw data, but it is highly vulnerable to Byzantine attacks.