A Continuized View on Nesterov Acceleration for Stochastic Gradient Descent and Randomized Gossip
This work addresses optimization and distributed computing challenges for machine learning and network systems, offering a novel analytical framework with practical applications.
The authors tackled the problem of analyzing and accelerating stochastic gradient descent and asynchronous gossip algorithms by introducing a continuized variant of Nesterov acceleration, which allows for differential calculus analysis and exact discretization with similar convergence rates, and they provided the first rigorous acceleration for asynchronous gossip algorithms.
We introduce the continuized Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradient steps at random times. This continuized variant benefits from the best of the continuous and the discrete frameworks: as a continuous process, one can use differential calculus to analyze convergence and obtain analytical expressions for the parameters; and a discretization of the continuized process can be computed exactly with convergence rates similar to those of Nesterov original acceleration. We show that the discretization has the same structure as Nesterov acceleration, but with random parameters. We provide continuized Nesterov acceleration under deterministic as well as stochastic gradients, with either additive or multiplicative noise. Finally, using our continuized framework and expressing the gossip averaging problem as the stochastic minimization of a certain energy function, we provide the first rigorous acceleration of asynchronous gossip algorithms.