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Gradient Descent Dynamics Explored in New Optimization Research

By PulseAugur Editorial · [2 sources] ·

Two new arXiv papers delve into the complexities of gradient descent algorithms. The first paper by Si Yi Meng examines gradient descent dynamics on logistic regression with non-separable data and large step sizes, revealing that while local convergence is often guaranteed, global convergence to a stable cycle can occur depending on initialization. The second paper, focusing on smooth convex optimization, establishes improved lower bounds for gradient descent acceleration beyond Nesterov's classical results, demonstrating a strict separation between non-anytime and anytime convergence rates. AI

IMPACT These theoretical explorations into gradient descent dynamics and optimization bounds could inform future algorithm development in machine learning.

RANK_REASON Two academic papers published on arXiv discussing theoretical aspects of gradient descent algorithms.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Gradient Descent Dynamics Explored in New Optimization Research

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Si Yi Meng, Antonio Orvieto, Daniel Yiming Cao, Christopher De Sa ·

    Gradient Descent on Logistic Regression with Non-Separable Data and Large Step Sizes

    arXiv:2406.05033v3 Announce Type: replace Abstract: We study gradient descent (GD) dynamics on logistic regression problems with large, constant step sizes. For linearly-separable data, it is known that GD converges to the minimizer with arbitrarily large step sizes, a property w…

  2. arXiv stat.ML TIER_1 Nederlands(NL) · Yuhan Ye, Kaizhao Liu ·

    Improved Gradient Descent Lower Bounds Beyond Nesterov

    arXiv:2609.02855v1 Announce Type: cross Abstract: We study how far gradient descent (GD) can be accelerated by predetermined stepsizes in smooth convex optimization. Going beyond the classical $\Omega(n^{-2})$ first-order oracle lower bound of Nemirovsky and Yudin, we prove an $\…

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