Quantum Mechanical Aspect in Bayesian Optimization

In this essay, we point out the quantum mechanical aspect in Bayesian Optimization: one might interpret Bayesian optimization as a process of computation in quantum mechanics, especially that of the molecular orbital method. We demonstrate that the optimization of the molecular structure and the refinement of the basis set is the process of Bayesian optimization, in which one should try to find better sampling points. The Bayesian optimization based upon the Gaussian process would be substituted by the molecular orbital computation by means of atomic orbitals of Gaussian functions. In addition, we propose a trick which would act as a sort of acquisition function. We give some examples in the polynomial optimization.