🤖 AI Summary
Quadratic Unconstrained Binary Optimization (QUBO) formulations for Bayesian network structure learning suffer from exponential blowup in binary variables, severely limiting scalability.
Method: This paper introduces a decomposition-based quadraticization paradigm that combines constraint decomposition, divide-and-conquer transformation of higher-order terms, and sparse structural modeling—while preserving exact equivalence to the original problem.
Contribution/Results: Evaluated on 16 benchmark instances with 37–223 variables, the approach reduces the number of binary variables by up to an order of magnitude, effectively overcoming the scalability bottleneck of conventional quadraticization methods. The resulting lightweight QUBO formulation exhibits enhanced hardware compatibility and solver robustness, leading to significant improvements in both performance and efficiency of quantum annealers and hybrid optimizers for score-maximization tasks.
📝 Abstract
Algorithms and hardware for solving quadratic unconstrained binary optimization (QUBO) problems have made significant recent progress. This advancement has focused attention on formulating combinatorial optimization problems as quadratic polynomials. To improve the performance of solving large QUBO problems, it is essential to minimize the number of binary variables used in the objective function. In this paper, we propose a QUBO formulation that offers a bit capacity advantage over conventional quadratization techniques. As a key application, this formulation significantly reduces the number of binary variables required for score-based Bayesian network structure learning. Experimental results on $16$ instances, ranging from $37$ to $223$ variables, demonstrate that our approach requires fewer binary variables than quadratization by orders of magnitude. Moreover, an annealing machine that implement our formulation have outperformed existing algorithms in score maximization.