Black-box optimization for integer-variable problems using Ising machines and factorization machines
This addresses integer-variable optimization for applications like hyperparameter tuning, but it is incremental as it extends existing binary methods to integers.
The paper tackled black-box optimization with integer variables by combining Ising machines and factorization machines with three encoding methods, and it successfully calculated the hydrogen molecule energy using all encodings, with one-hot encoding performing best for small problems.
Black-box optimization has potential in numerous applications such as hyperparameter optimization in machine learning and optimization in design of experiments. Ising machines are useful for binary optimization problems because variables can be represented by a single binary variable of Ising machines. However, conventional approaches using an Ising machine cannot handle black-box optimization problems with non-binary values. To overcome this limitation, we propose an approach for integer-variable black-box optimization problems by using Ising/annealing machines and factorization machines in cooperation with three different integer-encoding methods. The performance of our approach is numerically evaluated with different encoding methods using a simple problem of calculating the energy of the hydrogen molecule in the most stable state. The proposed approach can calculate the energy using any of the integer-encoding methods. However, one-hot encoding is useful for problems with a small size.