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Research questionFor non-separable logistic regression, when does constant-step gradient descent converge globally rather than enter a stable cycle?A step size can keep the solution locally stable while trajectories from other initializations fail to reach it. Instead, the iterates may settle into a stable periodic cycle.
Machine Learning
Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.Gradient Descent on Logistic Regression with Non-Separable Data and Large Step SizesThe analysis concerns constant-step gradient descent for non-separable logistic regression. It identifies a critical step size of 2/λ, where λ is the largest Hessian eigenvalue at the solution; in one dimension, steps below 1/λ guarantee global convergence, while constructed cycles occur between 1/λ and 2/λ, and in higher dimensions cycles can occur even below 1/λ. The behavior can depend on initialization.research paper · Sep 2, 2026
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