Non-Convex
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Related Articles from SNS
From Non-Convex to Strongly Convex: Curvature-Adaptive FTPL for Online Optimization
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. Recent work has shown that Follow-the-Perturbed-Leader (FTPL) achieves optimal $O(\sqrt{T})$ regret even for online non-convex Lipschitz losses, assuming access to an approximate offline-optimization oracle, but these guarantees do not exploit...
Lost in the Non-convex Loss Landscape: How to Fine-tune the Large Time Series Model?
Announce Type: new Abstract: Recently, large time series models (LTSMs) have gained increasing attention due to their similarities to large language models, including flexible context length, scalability, and task generality, outperforming advanced task-specific models. However, prior studies indicate that pre-trained LTSMs may exhibit a poorly conditioned non-convex loss landscape, leading to limited trainability. As a result, direct fine-tuning tends to cause overfitting and suboptimal...
Tracking the Effective Surface Area of Non-Convex Satellites
arXiv:2606.09439v1 Announce Type: new Abstract: This paper presents a novel framework to track the effective surface area of non-convex satellites, enabling the use of aerodynamic drag in low Earth orbit for orbital control. The proposed framework enables the satellite to track the effective surface area while simultaneously performing other maneuvers. We introduce this framework through a backstepping control algorithm, and exemplify its advantages with an extension, to simultaneously...
Tight Long-Term Tail Decay of (Clipped) SGD in Non-Convex Optimization
arXiv:2602.05657v2 Announce Type: replace Abstract: The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm. While many works provide high-probability guarantees, quantifying the error rate for a fixed probability threshold, there is a lack of work directly studying the probability of failure, i.e., quantifying the tail decay rate for a fixed error threshold. Moreover,...
Safeguarded Stochastic Polyak Step Sizes for Non-smooth Optimization: Robust Performance Without Small (Sub)Gradients
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. However, extensions of this approach to non-smooth settings remain in their early stages, often relying on interpolation assumptions or requiring knowledge of...
Secure RSMA-based Visible Light Networks under Spatial Correlation
Announce Type: replace Abstract: This paper investigates the secrecy sum rate (SSR) of rate-splitting multiple access (RSMA)-based visible light communication (VLC) systems considering internal eavesdropping, where legitimate users may intercept private data intended for others. We formulate an optimization problem to maximize the SSR of the system, which is inherently non-convex due to the complex coupling of the objective function and constraints. To this end, two different approaches...
Secure RSMA-based Visible Light Networks under Spatial Correlation
arXiv:2606.01941v1 Announce Type: new Abstract: This paper investigates the secrecy sum rate (SSR) of rate-splitting multiple access (RSMA)-based visible light communication (VLC) systems considering internal eavesdropping, where legitimate users may intercept private data intended for others. We formulate an optimization problem to maximize the SSR of the system, which is inherently non-convex due to the complex coupling of the objective function and constraints. To this end, two different...
Flatness and Generalization: Learning Multi-Index Models with Homogeneous Neural Networks
arXiv:2606.04429v1 Announce Type: cross Abstract: A common heuristic used to explain the generalization of first-order gradient methods on non-convex neural networks is that "flat interpolators generalize well" (Hochreiter and Schmidhuber, 1994; Keskar et al., 2017), where flatness can be measured by the trace of the Hessian of the empirical loss. However, Dinh et al. 2017) showed that, using symmetry of the network that can change flatness while keeping the population and empirical losses...
Robust and sparse support vector machine via hybrid truncated loss for supervised classification
Announce Type: new Abstract: The support vector machine (SVM) is a widely used classifier, but choosing an appropriate loss function remains difficult. Convex losses such as the hinge loss and least-squares loss are sensitive to outliers, while bounded non-convex losses often lead to high computational cost.
Iterative convergence in phase-field brittle fracture computations: exact line search is all you need
Announce Type: replace Abstract: Variational phase-field models of brittle fracture pose a local constrained minimization problem of a non-convex energy functional. In the discrete setting, the problem is most often solved by alternate minimization, exploiting the separate convexity of the energy with respect to the two unknowns. This approach is theoretically guaranteed to converge, provided each of the individual subproblems is solved successfully.