arXiv Machine Learning
Jul 9
Restricted Dynamic Geometric Complexity: Certificates for Structured Preconditioning
arXiv:2607. 07204v1 Announce Type: cross Abstract: Optimization geometrodynamics views optimizer state as evolving geometry.
Restricted Dynamic Geometric Complexity: Path-Space Reduction and M\"obius--Jacobi Response
arXiv:2607. 07204v2 Announce Type: replace-cross Abstract: Structured preconditioners restrict optimization to a small family of positive metrics, but endpoint condition-number reachability does not measure the geometric effort required to reach a useful metric.
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arXiv Machine Learning
Jul 9
Geometric--Nongeometric Optimizer Calculus: A Modular Language for Reachable Gradient Methods
arXiv:2607. 07206v1 Announce Type: new Abstract: Adaptive optimizers mix several mechanisms: a metric or preconditioner maps gradients to descent directions, while estimation, memory, step-size control, constraints, stochasticity, target modification, and discretization determine which directions are available and how they are used.
arXiv Machine Learning
Jul 9
Optimization Geometrodynamics: A Framework for Dynamic Geometric Optimization
arXiv:2607. 06723v1 Announce Type: cross Abstract: Most gradient-based optimization methods move parameters through a fixed background geometry, even when their internal states implicitly define changing notions of length, curvature, and preconditioning.
arXiv Machine Learning
Jul 14
Optimization Geometrodynamics: Variational Reduction and Interaction Curvature
arXiv:2607. 06723v2 Announce Type: replace-cross Abstract: Adaptive optimizers carry hidden states that change how visible gradients become parameter motion.
Hugging Face Trending Papers
Sep 3
Projected Riemannian Gradient Descent for the Bures-Wasserstein Barycenter: Dimension-Independent Linear Convergence at Unit Step Size
The paper introduces a Projected Riemannian Gradient Descent (RGD) algorithm for computing the Bures‑Wasserstein barycenter of positive definite matrices, achieving dimension‑independent linear convergence at unit step size. It resolves a previous dichotomy by showing that clipping eigenvalues to a fixed interval yields a closed‑form, non‑expansive projection in the BW metric, allowing the algorithm to match the empirical speed of unit‑step RGD while maintaining theoretical guarantees. The method also extends to the invariant matrix projection problem, providing a unified dimension‑independent analysis.
arXiv Machine Learning
Jul 28
When Rates Are Geometric: Rate-Certificate Transfer for Contact Splittings in Optimization
arXiv:2607. 23642v1 Announce Type: cross Abstract: Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm.
arXiv Machine Learning
Sep 4
Projected Riemannian Gradient Descent for the Bures-Wasserstein Barycenter: Dimension-Independent Linear Convergence at Unit Step Size
arXiv:2609. 03762v1 Announce Type: new Abstract: The computation of the Bures-Wasserstein (BW) barycenter of an ensemble of positive definite matrices arises throughout machine learning, optimal transport, and quantum information.
arXiv Machine Learning
Sep 16
Optimization over covariance matrices with a parameterized metric
arXiv:2609. 17089v1 Announce Type: cross Abstract: The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices.
arXiv Machine Learning
Jul 14
Lower Bound on the Cumulative Constrained Violation for the OGD+Projection algorithm for Constrained Online Convex Optimization (COCO)
arXiv:2607. 10808v1 Announce Type: new Abstract: The problem of constrained online convex optimization is considered, where at each round, once a learner commits to an action $x_t \in \mathcal{X} \subset \mathbb{R}^d$, a convex loss function $f_t$ and a convex constraint function $g_t$ that drives the constraint $g_t(x)\le 0$ are revealed.
Hugging Face Trending Papers
Aug 20
Unregularized Convergence of Single-Loop, Entropy-Regularized Natural Actor-Critic
While entropy regularization is widely used to stabilize and accelerate Natural Policy Gradient methods, its ability to yield faster convergence rates for the unregularized objective remains underexplored. Existing analyses often rely on double-loop architectures and invoke a linear entropy penalty.
arXiv Machine Learning
Sep 18
Stable Movement for Nondual Lipschitz Convex Optimization: Efficiency and Nearly Optimal Oracle Rates
arXiv:2609. 20701v1 Announce Type: cross Abstract: We study efficient algorithms for realizing the first-order oracle complexity of optimization of $G$-Lipschitz convex functions with respect to the $\ell_{q}$-norm over an $\ell_{p}$-ball of radius $R$, where $1\leq p,q\leq \infty$.
arXiv AI
Sep 10
Second-Order Smooth Planning with Optimal-Transport Bellman Smoothing
arXiv:2609.06484v1 Announce Type: cross Abstract: Planning with a generative model aims to estimate the value of a state using as few simulator calls as possible. SmoothCruiser achieves problem-indep...