On the Double Descent of Random Features Models Trained with SGD
This work provides theoretical insights into the double descent phenomenon for random features models, which is relevant for researchers in machine learning theory and practitioners using SGD in high-dimensional regression.
The authors tackled the generalization of random features regression trained with stochastic gradient descent (SGD) in high-dimensional settings, deriving non-asymptotic error bounds that show double descent behavior and proving that SGD generalizes well for interpolation learning with no loss in convergence rate compared to exact solutions.
We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/over-parameterized regime. In this work, we derive precise non-asymptotic error bounds of RF regression under both constant and polynomial-decay step-size SGD setting, and observe the double descent phenomenon both theoretically and empirically. Our analysis shows how to cope with multiple randomness sources of initialization, label noise, and data sampling (as well as stochastic gradients) with no closed-form solution, and also goes beyond the commonly-used Gaussian/spherical data assumption. Our theoretical results demonstrate that, with SGD training, RF regression still generalizes well for interpolation learning, and is able to characterize the double descent behavior by the unimodality of variance and monotonic decrease of bias. Besides, we also prove that the constant step-size SGD setting incurs no loss in convergence rate when compared to the exact minimum-norm interpolator, as a theoretical justification of using SGD in practice.