  This paper presents a comprehensive study on the convergence rates of the
stochastic gradient descent (SGD) algorithm when applied to overparameterized
two-layer neural networks. Our approach combines the Neural Tangent Kernel
(NTK) approximation with convergence analysis in the Reproducing Kernel Hilbert
Space (RKHS) generated by NTK, aiming to provide a deep understanding of the
convergence behavior of SGD in overparameterized two-layer neural networks. Our
research framework enables us to explore the intricate interplay between kernel
methods and optimization processes, shedding light on the optimization dynamics
and convergence properties of neural networks. In this study, we establish
sharp convergence rates for the last iterate of the SGD algorithm in
overparameterized two-layer neural networks. Additionally, we have made
significant advancements in relaxing the constraints on the number of neurons,
which have been reduced from exponential dependence to polynomial dependence on
the sample size or number of iterations. This improvement allows for more
flexibility in the design and scaling of neural networks, and will deepen our
theoretical understanding of neural network models trained with SGD.
