A black-box optimization algorithm such as Bayesian optimization finds extremum of an unknown function by alternating inference of the underlying function and optimization of an acquisition function. In a high-dimensional space, such algorithms perform poorly due to the difficulty of acquisition function optimization. Herein, we apply quantum annealing (QA) to overcome the difficulty in the continuous black-box optimization. As QA specializes in optimization of binary problems, a continuous vector has to be encoded to binary, and the solution of QA has to be translated back. Our method has the following three parts: 1) Random subspace coding based on axis-parallel hyperrectangles from continuous vector to binary vector. 2) A quadratic unconstrained binary optimization (QUBO) defined by acquisition function based on nonnegative-weighted linear regression model which is solved by QA. 3) A penalization scheme to ensure that the QA solution can be translated back. It is shown in benchmark tests that its performance using D-Wave Advantage$^{\rm TM}$ quantum annealer is competitive with a state-of-the-art method based on the Gaussian process in high-dimensional problems. Our method may open up a new possibility of quantum annealing and other QUBO solvers including quantum approximate optimization algorithm (QAOA) using a gated-quantum computers, and expand its range of application to continuous-valued problems.
翻译:Bayesian 优化等黑盒优化算法通过交替推断基本功能和优化获取函数的优化,发现一个未知功能的极端。 在高维空间中,由于获取功能优化的困难,这种算法运行不力。 在这里, 我们应用量安眠( QA) 来克服连续黑盒优化的难度。 当 QA 专门优化二进制问题时, 连续矢量必须编码为二进制, QA 的解决方案必须被翻译回来。 我们的方法有以下三个部分:1) 以直径双向矢量控函数为主的随机子空间连接。 在轴- 双向向矢量控函数为主的超矩形计算。 2) 以非负负负重量的线性回归模型定义的四进制双进式优化( QOBOBO) 定义的二次二次调整, 保证QA- QVP- QO- QO- QOrm 快速化算法为基数。