arXiv:2605. 08488v2 Announce Type: replace-cross Abstract: We develop a unified Lyapunov-integral quadratic constraint (IQC) framework for establishing uniform stability of first-order accelerated optimization algorithms in the $\beta$-smooth and $\gamma$-strongly convex regime.
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:2606. 11431v1 Announce Type: new Abstract: Mirror Descent (MD) extends Gradient Descent (GD) beyond Euclidean geometry and has recently reappeared as a lens for KL-regularized policy optimization in reinforcement learning and LLM post-training.
arXiv:2405. 00914v4 Announce Type: replace-cross Abstract: We present in this paper novel accelerated fully first-order methods in \emph{Bilevel Optimization} (BLO).
arXiv:2608.30431v1 Announce Type: cross Abstract: By focusing on algorithmic stability as a means of establishing out-of-sample bounds, we provide a system-theoretic interpretation of generalization...
arXiv:2406. 07746v4 Announce Type: replace-cross Abstract: We propose a computationally efficient algorithm that achieves anytime regret of order $\mathcal{O}(\sqrt{t})$, with explicit dependence on the system dimensions and on the solution of the Discrete Algebraic Riccati Equation (DARE).
arXiv:2609.13925v1 Announce Type: cross Abstract: This work studies the stability and convergence of augmented primal-dual dynamics when constraint values are estimated from samples. Unbiased constra...
arXiv:2609.30732v1 Announce Type: cross Abstract: We consider stochastic nonlinear optimization problems with deterministic equality constraints. While unconstrained stochastic optimization is well u...
arXiv:2606. 07088v1 Announce Type: new Abstract: Stochastic constrained decision-making requires optimizing performance objectives while enforcing statistical requirements such as safety or fairness.
The limited-memory BFGS (L-BFGS) algorithm is a cornerstone of large-scale optimization due to its linear memory and computational costs. However, in ill-conditioned or non-convex landscapes, the implicit inverse Hessian approximation can suffer from an exploding condition number, leading to numerical instability and degraded convergence.
arXiv:2609. 30501v1 Announce Type: new Abstract: Although bilevel optimization (BLO) has emerged as a powerful framework for addressing many complex and nested machine learning problems in recent years, most existing studies are confined to the lower-level strongly convex (LLSC) or lower-level generally convex (LLGC) settings (i.
arXiv:2607. 05836v1 Announce Type: cross Abstract: The limited-memory BFGS (L-BFGS) algorithm is a cornerstone of large-scale optimization due to its linear memory and computational costs.
arXiv:2406. 13041v3 Announce Type: replace Abstract: Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ sample complexity to find an $\varepsilon$-stationary point.