Nesterov acceleration despite very noisy gradients
This addresses a bottleneck in overparametrized machine learning by enabling faster convergence despite noisy gradients, though it is an incremental improvement over Nesterov's method.
The authors tackled the problem of accelerating gradient descent in the presence of noisy gradients, introducing AGNES, which provably achieves acceleration for smooth convex and strongly convex minimization tasks under any signal-to-noise ratio, improving on existing methods that require specific noise conditions.
We present a generalization of Nesterov's accelerated gradient descent algorithm. Our algorithm (AGNES) provably achieves acceleration for smooth convex and strongly convex minimization tasks with noisy gradient estimates if the noise intensity is proportional to the magnitude of the gradient at every point. Nesterov's method converges at an accelerated rate if the constant of proportionality is below 1, while AGNES accommodates any signal-to-noise ratio. The noise model is motivated by applications in overparametrized machine learning. AGNES requires only two parameters in convex and three in strongly convex minimization tasks, improving on existing methods. We further provide clear geometric interpretations and heuristics for the choice of parameters.