Stochastic Mirror Descent in Average Ensemble Models
This work provides theoretical insights into training algorithms for ensemble models, but it is incremental as it extends known SGD results to a broader class of methods without demonstrating broad SOTA improvements.
The paper tackles the performance of stochastic mirror descent (SMD) in mean-field ensemble models, generalizing earlier SGD results by deriving a nonlinear PDE for the asymptotic distribution evolution and showing the mirror potential's impact through a multiplicative term interpretable as a gradient flow on a Riemannian manifold, with numerical simulations characterizing its effect on binary classification tasks.
The stochastic mirror descent (SMD) algorithm is a general class of training algorithms, which includes the celebrated stochastic gradient descent (SGD), as a special case. It utilizes a mirror potential to influence the implicit bias of the training algorithm. In this paper we explore the performance of the SMD iterates on mean-field ensemble models. Our results generalize earlier ones obtained for SGD on such models. The evolution of the distribution of parameters is mapped to a continuous time process in the space of probability distributions. Our main result gives a nonlinear partial differential equation to which the continuous time process converges in the asymptotic regime of large networks. The impact of the mirror potential appears through a multiplicative term that is equal to the inverse of its Hessian and which can be interpreted as defining a gradient flow over an appropriately defined Riemannian manifold. We provide numerical simulations which allow us to study and characterize the effect of the mirror potential on the performance of networks trained with SMD for some binary classification problems.