Generalization Bounds for Label Noise Stochastic Gradient Descent

Jung Eun Huh

Abstract: We develop generalization error bounds for stochastic gradient descent (SGD) with label noise in non-convex settings under uniform dissipativity and smoothness conditions. Under a suitable choice of semimetric, we establish a contraction in Wasserstein distance of the label noise stochastic gradient flow that depends polynomially on the parameter dimension d. Using the framework of algorithmic stability, we derive time-independent generalisation error bounds for the discretized algorithm with a constant learning rate. The error bound we achieve scales polynomially with $d$ and with the rate of $n^{−2/3}$, where n is the sample size. This rate is better than the best-known rate of $n^{−1/2}$ established for stochastic gradient Langevin dynamics (SGLD)—which employs parameter-independent Gaussian noise—under similar conditions. Our analysis offers quantitative insights into the effect of label noise.