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First-Order Optimization Algorithms via Discretization of Finite-Time Convergent Flows

In this paper, we investigate in the context of deep neural networks, the performance of several discretization algorithms for two first-order finite-time optimization flows. These flows are, namely, the rescaled-gradient flow (RGF) and the signed-gradient flow (SGF), and consist of non-Lipscthiz or discontinuous dynamical systems that converge locally in finite time to the minima of gradient-dominated functions. We introduce three discretization methods for these first-order finite-time flows, and provide convergence guarantees. We then apply the proposed algorithms in training neural networks and empirically test their performances on three standard datasets, namely, CIFAR10, SVHN, and MNIST. Our results show that our schemes demonstrate faster convergences against standard optimization alternatives, while achieving equivalent or better accuracy.

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