Stochastic Learning Equation using Monotone Increasing Resolution of Quantization

TL;DR

This paper introduces a stochastic learning equation with a monotone increasing quantization resolution, demonstrating convergence under a distributional perspective and enabling global optimization for Lipschitz domains.

Contribution

It presents a novel quantized learning algorithm with increasing resolution and provides a stochastic analysis showing convergence and global optimization capabilities.

Findings

Quantization error modeled as i.i.d. white noise under certain hypotheses.

Convergence of the proposed learning equation is established in a weak sense.

Global optimization is achievable in Lipschitz domains, not just local minima.

Abstract

In this paper, we propose a quantized learning equation with a monotone increasing resolution of quantization and stochastic analysis for the proposed algorithm. According to the white noise hypothesis for the quantization error with dense and uniform distribution, we can regard the quantization error as i.i.d.\ white noise. Based on this, we show that the learning equation with monotonically increasing quantization resolution converges weakly as the distribution viewpoint. The analysis of this paper shows that global optimization is possible for a domain that satisfies the Lipschitz condition instead of local convergence properties such as the Hessian constraint of the objective function.