Efficient correlation-based discretization of continuous variables for annealing machines

TL;DR

This paper introduces a correlation-based discretization method for continuous variables tailored for annealing machines, effectively reducing binary variable count in QUBO formulations while maintaining prediction accuracy.

Contribution

The paper proposes a novel correlation-based discretization technique that minimizes binary variables needed for annealing machines, improving efficiency over simple binary expansion methods.

Findings

Reduces the number of binary variables in QUBO formulations.

Maintains prediction accuracy with fewer variables.

Demonstrates effectiveness through numerical experiments.

Abstract

Annealing machines specialized for combinatorial optimization problems have been developed, and some companies offer services to use those machines. Such specialized machines can only handle binary variables, and their input format is the quadratic unconstrained binary optimization (QUBO) formulation. Therefore, discretization is necessary to solve problems with continuous variables. However, there is a severe constraint on the number of binary variables with such machines. Although the simple binary expansion in the previous research requires many binary variables, we need to reduce the number of such variables in the QUBO formulation due to the constraint. We propose a discretization method that involves using correlations of continuous variables. We numerically show that the proposed method reduces the number of necessary binary variables in the QUBO formulation without a significant loss in prediction accuracy.