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Stochastic Polyak Step-sizes and Momentum: Convergence Guarantees and Practical Performance
Dimitris Oikonomou, Nicolas Loizou
https://arxiv.org/abs/2406.04142

Stochastic Polyak Step-sizes and Momentum: Convergence Guarantees and Practical Performance
Stochastic gradient descent with momentum, also known as Stochastic Heavy Ball method (SHB), is one of the most popular algorithms for solving large-scale stochastic optimization problems in various machine learning tasks. In practical scenarios, tuning the step-size and momentum parameters of the method is a prohibitively expensive and time-consuming process. In this work, inspired by the recent advantages of stochastic Polyak step-size in the performance of stochastic gradient descent (SGD), …

Parameterization of Stochasticity in Galaxy Clustering and Reconstruction of Tomographic Matter Clustering
Shuren Zhou, Pengjie Zhang
https://arxiv.org/abs/2406.03018

Parameterization of Stochasticity in Galaxy Clustering and Reconstruction of Tomographic Matter Clustering
The stochasticity in galaxy clustering, the mismatch between galaxy and underlying matter distribution, suppresses the matter clustering amplitude reconstructed by the combination of galaxy auto-correlation and galaxy-galaxy lensing cross-correlation. In this work, we solve the stochasticity systematics by parameterizing the cross correlation coefficient $r(k)$ between galaxy and matter. We investigate the performance of 12 kinds of parameterization schemes, against the cosmoDC2 $\&$ TNG300-1 g…

US VC firms are putting pressure on tech startups to ask their Chinese backers to divest as VCs anticipate tighter controls on foreign ownership from Washington (Eleanor Olcott/Financial Times)
https://t.co/J70od5P8PP

Prominence and coronal rain formation by steady versus stochastic heating and how we can relate it to observations
V. Jer\v{c}i\'c (Centre for mathematical Plasma-Astrophysics, KU Leuven, Belgium), J. M. Jenkins (Centre for mathematical Plasma-Astrophysics, KU Leuven, Belgium), R. Keppens (Centre for mathematical Plasma-Astrophysics, KU Leuven, Belgium)

Prominence and coronal rain formation by steady versus stochastic heating and how we can relate it to observations
Prominences and coronal rain are two forms of coronal condensations for which we still lack satisfactory details on the formation pathways and conditions under which the two come to exist. We compared prominences that formed via a steady versus stochastic type of heating. We performed 2.5D simulations using the open-source MPI-AMRVAC code. To further extend the work and allow for future direct comparison with observations, we used Lightweaver to form spectra of the filament view of our steady c…

Private Stochastic Convex Optimization with Heavy Tails: Near-Optimality from Simple Reductions
Hilal Asi, Daogao Liu, Kevin Tian
https://arxiv.org/abs/2406.02789

Private Stochastic Convex Optimization with Heavy Tails: Near-Optimality from Simple Reductions
We study the problem of differentially private stochastic convex optimization (DP-SCO) with heavy-tailed gradients, where we assume a $k^{\text{th}}$-moment bound on the Lipschitz constants of sample functions rather than a uniform bound. We propose a new reduction-based approach that enables us to obtain the first optimal rates (up to logarithmic factors) in the heavy-tailed setting, achieving error $G_2 \cdot \frac 1 {\sqrt n} + G_k \cdot (\frac{\sqrt d}{nε})^{1 - \frac 1 k}$ under $(ε, δ)…

Stochastic Dynamic Network Utility Maximization with Application to Disaster Response
Anna Scaglione, Nurullah Karakoc
https://arxiv.org/abs/2406.03750 htt…

Stochastic Dynamic Network Utility Maximization with Application to Disaster Response
In this paper, we are interested in solving Network Utility Maximization (NUM) problems whose underlying local utilities and constraints depend on a complex stochastic dynamic environment. While the general model applies broadly, this work is motivated by resource sharing during disasters concurrently occurring in multiple areas. In such situations, hierarchical layers of Incident Command Systems (ICS) are engaged; specifically, a central entity (e.g., the federal government) typically coordina…

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Projection-Free Variance Reduction Methods for Stochastic Constrained Multi-Level Compositional Optimization
Wei Jiang, Sifan Yang, Wenhao Yang, Yibo Wang, Yuanyu Wan, Lijun Zhang
https://arxiv.org/abs/2406.03787

Projection-Free Variance Reduction Methods for Stochastic Constrained Multi-Level Compositional Optimization
This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex. Existing projection-free algorithms for solving this problem suffer from two limitations: 1) they solely focus on the gradient mapping criterion and fail to match the optimal sample complexities in unconstrained settings; 2) their analysis is exclusively appl…