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:2610.07290v1 Announce Type: cross Abstract: Recent advances in penalty-based methods for stochastic bilevel optimization (SBO) have eliminated the need for second-order derivative oracles. Howe...
arXiv:2502.21099v3 Announce Type: replace-cross Abstract: This paper proposes {\sf AEPG-SPIDER}, an Adaptive Extrapolated Proximal Gradient (AEPG) method with variance reduction for minimizing compos...
arXiv:2605. 15350v2 Announce Type: replace-cross Abstract: Stochastic compositional optimization minimizes $F(f(x), x)$ over a compact convex set when the inner map $f$ is available only through noisy samples.
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.
arXiv:2605.05660v3 Announce Type: replace Abstract: Multi-objective optimization (MOO) has received growing attention in applications that require learning under multiple criteria. However, most exis...
arXiv:2603. 10485v3 Announce Type: replace-cross Abstract: In this work, we study the convergence properties of the Dual Space Preconditioned Gradient Descent, encompassing optimizers such as Normalized Gradient Descent and Gradient Clipping.
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...
The paper introduces a novel technique called "persistence of memory" to enhance stochastic subspace methods for large‑scale optimisation. By using a weakly correlated guidance vector that is refreshed only at wide intervals, the method provides a structured direction for random subspace descent. The authors demonstrate that this guidance can be efficiently computed in sparse or minibatch settings and present the first theoretical analysis of classical SSD methods for sparse functions, showing alignment with low‑lying Hessian eigenvectors near the optimum.
arXiv:2607. 15412v1 Announce Type: new Abstract: Multi-objective learning (MOL) aims to optimize multiple objectives simultaneously.
The paper addresses bias introduced by aggregating local signs in distributed sign-based variance reduction methods, which hampers optimal convergence rates. By proposing an unbiased compression of recursive gradient increments to track the global gradient at the server, the authors achieve optimal convergence rates for both nonconvex stochastic and finite-sum optimization. They provide specific rate bounds for α-norms and demonstrate matching sample complexities to centralized settings for finite-sum problems.
arXiv:2307. 07113v2 Announce Type: replace-cross Abstract: In this paper, we consider the decentralized, stochastic nonconvex strongly-concave (NCSC) minimax problem with nonsmooth regularization terms on both primal and dual variables, wherein a network of $m$ computing agents collaborate via peer-to-peer communications.