Accelerating SGDM via Learning Rate and Batch Size Schedules: A Lyapunov-Based Analysis

תקציר מקורי באנגליתarXiv:2508.03105v3 Announce Type: replace Abstract: We analyze the convergence behavior of stochastic gradient descent with momentum (SGDM) under dynamic learning-rate and batch-size schedules by introducing a novel and simpler Lyapunov function. We extend the existing theoretical framework to cover three practical scheduling strategies commonly used in deep learning: a constant batch size with a decaying learning rate, an increasing batch size with a decaying learning rate, and an increasing batch size with an increasing learning rate. Our results reveal a clear hierarchy in convergence: a constant batch size does not guarantee convergence of the expected gradient norm under our Lyapunov-based analysis, whereas an increasing batch size does, and simultaneously increasing both the batch si