Convex Optimization
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Related Articles from SNS
Near-Optimal Decentralized Stochastic Convex Optimization over Networks
arXiv:2606.04757v1 Announce Type: cross Abstract: We study decentralized stochastic smooth convex optimization, where $M$ workers minimize an average objective using local stochastic gradients and neighbor-only communication over a fixed gossip network. A central question in this setting is to determine the largest number of workers that can be used under a total budget of $N$ gradient samples while still preserving the centralized $O(1/\sqrt N)$ statistical rate. We introduce an accelerated...
A Global Convergence Analysis of Consensus ALADIN for Convex Optimization
arXiv:2606.08112v1 Announce Type: new Abstract: Distributed optimization problems are pervasive in machine learning and optimal control. In this paper, we study smooth strongly convex distributed consensus optimization problems.
Noise-Adaptive High-Probability Regret Bounds for Online Convex Optimization
arXiv:2606.08028v1 Announce Type: new Abstract: We study high-probability regret bounds for online convex optimization (OCO) with strongly convex losses and establish three results that resolve open questions at the intersection of noise adaptivity, feedback structure, and constraint satisfaction. For the full-information setting with sub-Gaussian stochastic gradients, we prove a noise-adaptive high-probability regret bound in which the martingale deviation term scales with the noise level...
The Sample Complexity of Parameter-Free Stochastic Convex Optimization
Announce Type: replace Abstract: We study the sample complexity of stochastic convex optimization when problem parameters such as the distance to optimality and the Lipschitz constant are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting to the validation set.
LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization
arXiv:2606.08993v1 Announce Type: new Abstract: We propose LEAF, a learning-enabled ADMM framework for accelerated convex optimization. The key idea is to approximate the Moreau envelope of the objective function using an Input Convex Neural Network (ICNN), resulting in a learned model that preserves convexity and smoothness. This leads to the proposed Moreau Envelope Learning ADMM (MEL-ADMM) and its splitting variant sMEL-ADMM.
Accelerated Decentralized Stochastic Gradient Descent for Strongly Convex Optimization
Announce Type: new Abstract: Decentralized stochastic optimization is a fundamental paradigm for large-scale learning over networks, where agents communicate only with their neighbors and no central coordinator is required. For strongly convex problems, communication efficiency is mainly determined by the condition number \(\kappa=L/\mu\) and the network spectral gap \(1-\beta\). Although deterministic decentralized methods can simultaneously achieve accelerated \(\sqrt{\kappa}\) and...
OCO-S$^2$: Online Convex Optimization with Stateful Costs and Sparse Communication
Announce Type: replace Abstract: We study \textsc{OCO-S$^2$}, an online convex optimization setting in which decisions drive a stable dynamical state, losses are incurred along the induced state trajectory, and first-order feedback is available only through sparse block communication with partial participation. This coupling creates a dynamic-regret problem beyond pointwise OCO: the learner updates and holds decisions at the block scale, whereas the hindsight comparator may vary at the...
One-Shot Klein Cutting Planes for Lipschitz Geodesically Convex Optimization in Hyperbolic Space
arXiv:2605.17540v4 Announce Type: replace Abstract: Motivated by the COLT 2023 open problem of Criscitiello, Mart\'inez-Rubio, and Boumal on deterministic first-order methods for Lipschitz geodesically convex optimization on Hadamard manifolds, we study hyperbolic space \[ \HH^d_{-\kappaC^2} =\{X\in\R^{d+1}:\ipL{X}{X}=-1,\ X_0>0\}, \qquad \ip{U}{V}_X=\kappaC^{-2}\ipL{U}{V}. For every geodesically convex $M$-Lipschitz function \[ f:\bar B_{\HH}(x_0,r)\to\R,\qquad s=\kappaC r, \] we give a...
BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization
arXiv:2605.23937v2 Announce Type: replace Abstract: Knowledge base (KB) embeddings aim at combining the capability of classical knowledge graph embeddings to generalize the information present in facts, the ABox, with conceptual knowledge represented in an ontology language, the TBox. Several authors have recently explored the idea of mapping concepts to convex regions in a vector space. This is useful to represent hierarchies, typically present in TBoxes, since more general concepts can be...
Adaptive Metrics for Norm-Minimization-Based Outer Approximation in Convex Vector Optimization
Announce Type: replace-cross Abstract: We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation error in a fixed Euclidean norm. This enables the algorithm to exploit problem geometry dynamically.