Improving search efficiency via adaptive acquisition function selection in discrete black-box optimization

Abstract

In discrete-variable black-box optimization, the number of candidate solutions grows combinatorially, while each evaluation is often expensive. Therefore, it is important to identify promising solutions efficiently within a limited number of trials. Bayesian Optimization of Combinatorial Structures (BOCS), an existing parametric method, works effectively when only a small amount of data is available. However, as the number of observations increases, BOCS tends to repeatedly propose points that have already been evaluated, which leads to search stagnation. A random-point addition strategy has been proposed to address this issue when an evaluated point is proposed, but it cannot sufficiently exploit information from promising data obtained so far. In this study, we propose a hybrid method that uses BOCS as the main search framework and generates alternative unevaluated points using a Gaussian process only when search stagnation is detected. In the Gaussian-process-based component, multiple Lower Confidence Bound (LCB) acquisition functions are adaptively selected to dynamically control the balance between exploitation and exploration. Numerical experiments using fully connected Quadratic Unconstrained Binary Optimization (QUBO) and Higher-order Unconstrained Binary Optimization (HUBO) as black-box functions show that the proposed method finds solutions with better objective values than the conventional random-point addition method in both settings. Additional analyses show that its effectiveness comes from selecting points that promote search progress within Hamming-distance neighborhoods, rather than simply adding low-energy points near promising solutions. Experiments with sparse surrogate models for quantum annealer applications further suggest the importance of retaining near-fully connected representational capacity.