Intuitive Analysis of the Quantization-based Optimization: From Stochastic and Quantum Mechanical Perspective

TL;DR

This paper introduces a novel optimization approach based on quantization, linking it to thermodynamic and quantum mechanics, and demonstrates its effectiveness through simulations on benchmark functions.

Contribution

It presents an intuitive analysis and a stochastic differential equation model for quantization-based optimization, connecting it to thermodynamics and quantum mechanics.

Findings

Quantization reduces the number of saddle points and local minima.

The proposed method outperforms traditional nonlinear optimization techniques.

Simulation results validate the effectiveness of quantization-based optimization.

Abstract

In this paper, we present an intuitive analysis of the optimization technique based on the quantization of an objective function. Quantization of an objective function is an effective optimization methodology that decreases the measure of a level set containing several saddle points and local minima and finds the optimal point at the limit level set. To investigate the dynamics of quantization-based optimization, we derive an overdamped Langevin dynamics model from an intuitive analysis to minimize the level set by iterative quantization. We claim that quantization-based optimization involves the quantities of thermodynamical and quantum mechanical optimization as the core methodologies of global optimization. Furthermore, on the basis of the proposed SDE, we provide thermodynamic and quantum mechanical analysis with Witten-Laplacian. The simulation results with the benchmark functions, which compare the performance of the nonlinear optimization, demonstrate the validity of the quantization-based optimization.