A black-box optimization method with polynomial-based kernels and quadratic-optimization annealing

TL;DR

Kernel-QA is a novel black-box optimization method that uses polynomial kernels within a QUBO framework, efficiently leveraging Ising machines for high-dimensional, multi-modal functions.

Contribution

It introduces a new surrogate modeling approach with polynomial kernels in a QUBO setting, enabling scalable and effective black-box optimization.

Findings

Effective on high-dimensional, multi-modal landscapes

Demonstrates robustness in local minima scenarios

Scalable to 80-dimensional real variables and 640 binary variables

Abstract

We introduce kernel-QA, a black-box optimization (BBO) method that constructs surrogate models analytically using low-order polynomial kernels within a quadratic unconstrained binary optimization (QUBO) framework, enabling efficient utilization of Ising machines. The method has been evaluated on artificial landscapes, ranging from uni-modal to multi-modal, with input dimensions extending to 80 for real variables and 640 for binary variables. The results demonstrate that kernel-QA is particularly effective for optimizing black-box functions characterized by local minima and high-dimensional inputs, showcasing its potential as a robust and scalable BBO approach.