Learning-rate-free Momentum SGD with Reshuffling Converges in Nonsmooth Nonconvex Optimization

TL;DR

This paper introduces a new learning-rate-free momentum SGD framework with convergence guarantees for nonsmooth nonconvex optimization, particularly effective for training nonsmooth neural networks, supported by theoretical proofs and preliminary experiments.

Contribution

It presents a novel adaptive framework for learning-rate-free momentum SGD with proven convergence in nonsmooth nonconvex settings, advancing training methods for neural networks.

Findings

The framework guarantees convergence to stationary points.

The proposed LFM method performs comparably to state-of-the-art methods.

Preliminary experiments validate the effectiveness of LFM.

Abstract

In this paper, we propose a generalized framework for developing learning-rate-free momentum stochastic gradient descent (SGD) methods in the minimization of nonsmooth nonconvex functions, especially in training nonsmooth neural networks. Our framework adaptively generates learning rates based on the historical data of stochastic subgradients and iterates. Under mild conditions, we prove that our proposed framework enjoys global convergence to the stationary points of the objective function in the sense of the conservative field, hence providing convergence guarantees for training nonsmooth neural networks. Based on our proposed framework, we propose a novel learning-rate-free momentum SGD method (LFM). Preliminary numerical experiments reveal that LFM performs comparably to the state-of-the-art learning-rate-free methods (which have not been shown theoretically to be convergence) across well-known neural network training benchmarks.