arXiv Machine Learning
Jul 15
A Geometric Approach to Constrained Online Learning
arXiv:2605. 21107v2 Announce Type: replace Abstract: We study constrained online convex optimization with adversarial time-varying constraints.
From Non-Convex to Strongly Convex: Curvature-Adaptive FTPL for Online Optimization
arXiv:2606. 02948v1 Announce Type: new Abstract: Curvature adaptivity is a classical theme in online optimization: for convex Lipschitz losses, adaptive methods interpolate between the optimal $O(\sqrt{T})$ regret for general convex losses and $O(\log T)$ regret under strong convexity.
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arXiv Machine Learning
Jul 23
Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions
arXiv:2607. 20316v1 Announce Type: cross Abstract: We study decentralized online optimization for strongly geodesically convex (strongly g-convex) losses on Riemannian manifolds with bounded sectional curvature, including positively curved manifolds.
arXiv Machine Learning
Jul 28
Learning from the Descent Direction: Adaptive Gradient Descent under One-Sided H\"older Regularity
arXiv:2607. 22906v1 Announce Type: new Abstract: We study adaptive gradient descent for continuously differentiable, possibly nonconvex objectives under one-sided H\"older regularity.
arXiv Machine Learning
6d ago
Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size
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 Machine Learning
1d ago
Online Convex Optimization with Dueling Feedback
arXiv:2608. 15050v1 Announce Type: new Abstract: We study online convex optimization with dueling (pairwise comparison) feedback, where the learner observes only a binary preference between two queried points.
arXiv Machine Learning
Jun 9
Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds
arXiv:2509. 07779v2 Announce Type: replace-cross Abstract: We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting.
arXiv Machine Learning
Jun 3
Online Learning with Gradient-Variation Interval Regret
arXiv:2606. 03831v1 Announce Type: new Abstract: This paper investigates non-stationary online learning using the metric of interval regret, which requires an online algorithm to perform well over every time interval.
arXiv Machine Learning
Jul 28
Gradient-Variation Regret Bounds for Unconstrained Online Learning
arXiv:2604. 11151v2 Announce Type: replace Abstract: We develop parameter-free algorithms for unconstrained online learning with regret guarantees that scale with the gradient variation $V_T(u) = \sum_{t=2}^T \|\nabla f_t(u)-\nabla f_{t-1}(u)\|^2$.
arXiv Machine Learning
Jul 21
Optimizing the Preconditioner: A Black-box Online-to-Nonconvex Conversion with Static Regret Minimization Oracles
arXiv:2607. 17607v1 Announce Type: new Abstract: We study whether stochastic nonconvex optimization can be reduced to ordinary static regret minimization in online convex optimization in a black-box manner.
arXiv Machine Learning
Jul 17
What's in a Smoothness Constant? Tighter Rates for Local SGD with Bounded Second-order Heterogeneity
arXiv:2607. 14731v1 Announce Type: new Abstract: Local SGD, also known as Federated Averaging, is a widely used distributed optimization algorithm.
arXiv Machine Learning
Jun 30
Curvature-Weighted Gradient Diversity: A Noise Measure for Geometry-Adaptive SGD Schedules
arXiv:2606. 30455v1 Announce Type: new Abstract: The standard convergence analysis of mini-batch stochastic gradient descent (SGD) models gradient noise using a single variance term that treats all parameter directions equally, ignoring the fact that noise in high-curvature directions has less impact because learning rates are already constrained there.
arXiv Machine Learning
Aug 4
A Perturbation Approach to Unconstrained Linear Bandits
arXiv:2603. 28201v3 Announce Type: replace Abstract: We revisit the standard perturbation-based approach of Abernethy et al.