The paper investigates two strategies for incorporating heterogeneous node weights in decentralized learning: embedding the weights into local losses to use a doubly stochastic matrix, and keeping the original losses while using a λ‑induced row‑stochastic matrix. By developing a weighted Hilbert‑space framework, the authors derive tighter convergence rates and show that the row‑stochastic matrix becomes self‑adjoint, reducing penalty terms that otherwise amplify consensus error. They provide conditions under which the row‑stochastic design converges faster, even with a smaller spectral gap, and offer topology‑design guidelines based on eigenvalue comparisons.
arXiv:2606. 09154v1 Announce Type: new Abstract: Decentralized SGD is a fundamental algorithm in decentralized learning, although the influence of an underlying network topology on its convergence behavior is not yet fully understood.
arXiv:2606. 07496v1 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.
arXiv:2606. 19411v1 Announce Type: new Abstract: Selecting a small, diverse, high-quality subset from a massive pool of candidates is a recurring primitive in modern machine learning -- data curation and coreset selection for training and fine-tuning large models, active-learning batch acquisition, prompt and exemplar selection for in-context learning, retrieval diversification, and experimental design.
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.
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:2608.22636v1 Announce Type: cross Abstract: Q-learning with linear function approximation can be unstable because an arbitrary approximation architecture need not preserve the Bellman contracti...
arXiv:2607. 15412v1 Announce Type: new Abstract: Multi-objective learning (MOL) aims to optimize multiple objectives simultaneously.
arXiv:2605. 18528v2 Announce Type: replace-cross Abstract: A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized.
arXiv:2609.14953v1 Announce Type: cross Abstract: This paper aims to develop new and efficient distributed algorithms for solving a class of monotone inclusions, $0 \in \sum_{i=1}^n (G_ix + T_ix)$, o...
arXiv:2608. 03001v1 Announce Type: cross Abstract: Unit excitation (UE) is a common assumption in stochastic saddle avoidance: the stochastic error must have a uniformly positive component along every direction, in expectation.
arXiv:2509. 08726v3 Announce Type: replace-cross Abstract: This paper focuses on the decentralized stochastic optimization problem $f(\mathbf{x})=\frac{1}{m}\sum_{i=1}^m f_i(\mathbf{x})$ over a connected network of $n$ agents, where each local function has the form of $f_i(\mathbf{x}) = {\mathbb E}\left[F(\mathbf{x};{\boldsymbol \xi}_i)\right]$ which satisfies the $(L_0,L_1)$-smooth condition but possibly nonconvex and each random variable ${\boldsymbol \xi}_i$ follows distribution ${\mathcal D}_i$.
arXiv:2608. 02375v1 Announce Type: cross Abstract: This paper studies the distributed online control problem over a network of linear time-invariant (LTI) systems in the presence of adversarial disturbances and time-varying convex costs.