Efficient correlation-based discretization of continuous variables for annealing machines
This work addresses a bottleneck for users of annealing machines in combinatorial optimization, though it appears incremental as it builds on prior discretization methods.
The paper tackles the problem of discretizing continuous variables for annealing machines, which are constrained to binary variables, by proposing a correlation-based method that reduces the number of binary variables needed without significantly compromising prediction accuracy.
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.