math.OC · 2026-09-16 · No. 115

Optimization and Control, 2026-09-16.

2 new papers in math.OC. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

2 entries
  1. 01

    Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult

    Alexander Tyurin

    math.OC · cs.LG

    Modern large-scale machine learning tasks often require multiple workers, devices, CPUs, or GPUs to compute stochastic gradients in parallel and asynchronously to train model weights. Theoretical results typically distinguish between two settings: (i) the homogeneous setting, where all workers have access to the same data distribution, and (ii) the heterogeneous setting, where each worker operates on different data distributions. Known...

    arxiv.org/abs/2609.17483 · PDF

  2. 02

    Optimization over covariance matrices with a parameterized metric

    Yibang Li, Bamdev Mishra, Pratik Jawanpuria, Cyrus Mostajeran

    math.OC · cs.LG

    The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices. Euclidean, Bures-Wasserstein and affine-invariant metrics are common choices, but their relative effectiveness depends on the objective. We introduce a two-parameter family defined by $X^{p}LX^{q}+X^{q}LX^{p}=U$, solved for $L$ at each tangent vector $U$, that contains all three as exact members, at $(0,0)$, $(1,0)$...

    arxiv.org/abs/2609.17089 · PDF

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