arXiv:2307. 10053v5 Announce Type: replace-cross Abstract: In this paper, we focus on providing convergence guarantees for stochastic subgradient methods in minimizing nonsmooth nonconvex functions.
arXiv:2607. 01755v1 Announce Type: cross Abstract: In this paper, we consider the nonsmooth nonconvex decentralized optimization problem, where inter-agent communication is compressed.
arXiv:2504. 09951v2 Announce Type: replace-cross Abstract: We revisit a classical assumption for analyzing stochastic gradient algorithms where the squared norm of the stochastic subgradient (or the variance for smooth problems) is allowed to grow as fast as the squared norm of the optimization variable.
In this paper, we consider the nonsmooth nonconvex decentralized optimization problem, where inter-agent communication is compressed. We propose a general framework that unifies various decentralized stochastic subgradient-type methods with unbiased compression and contractive compression with error compensation.
arXiv:2607. 06883v1 Announce Type: cross Abstract: We consider the problem of finding stationary points for stochastic convex optimization problems.
arXiv:2512. 02342v3 Announce Type: replace-cross Abstract: The stochastic Polyak step size (SPS) has proven to be a promising choice for stochastic gradient descent (SGD), delivering competitive performance relative to state-of-the-art methods on smooth convex and non-convex optimization problems, including deep neural network training.
arXiv:2608. 05460v1 Announce Type: cross Abstract: This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function.
arXiv:2608. 03001v1 Announce Type: cross Abstract: Unit excitation (UE) is a common assumption in stochastic saddle avoidance: the stochastic error must have a uniformly positive component along every direction, in expectation.
The paper investigates Polyak-type step-size strategies for extragradient methods applied to deterministic and stochastic monotone root-finding problems. It shows that the projection-based correction in deterministic extragradient can be derived by minimizing an upper bound on the distance to a solution, mirroring classical Polyak step-size construction. The authors provide a unified deterministic analysis that does not require global Lipschitz continuity, achieving sublinear convergence under H"older or “(L0, L1)-Lipschitz” conditions and linear convergence with strong monotonicity, and extend the approach to stochastic settings with both direct and decreasing step-size variants.
arXiv:2606. 24879v1 Announce Type: cross Abstract: We study the last iterate of the stochastic subgradient method for one-dimensional convex Lipschitz objectives.
Unit excitation (UE) is a common assumption in stochastic saddle avoidance: the stochastic error must have a uniformly positive component along every direction, in expectation. This condition gives a direct way to rule out convergence to strict saddles, but it also oversimplifies the actual noise structure, and does not match many stochastic optimization regimes.
arXiv:2609.15257v1 Announce Type: cross Abstract: We analyze a stochastic algorithm with Halpern anchoring for constrained convex-concave problems and monotone variational inequalities. This algorith...
arXiv:2510.11676v2 Announce Type: replace-cross Abstract: We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex fu...