Many real-life problems require optimizing functions with expensive evaluations. Bayesian Optimization (BO) and Search-based Optimization (SO) are two broad families of algorithms that try to find the global optima of a function with the goal of minimizing the number of function evaluations. A large body of existing work deals with the single-fidelity setting, where function evaluations are very expensive but accurate. However, in many applications, we have access to multiple-fidelity functions that vary in their cost and accuracy of evaluation. In this paper, we propose a novel approach called Multi-fidelity Hybrid (MF-Hybrid) that combines the best attributes of both BO and SO methods to discover the global optima of a black-box function with minimal cost. Our experiments on multiple benchmark functions show that the MF-Hybrid algorithm outperforms existing single-fidelity and multi-fidelity optimization algorithms.

This paper considers global optimization with a black-box unknown objective function that can be non-convex and non-differentiable. Such a difficult optimization problem arises in many real-world applications, such as parameter tuning in machine learning, engineering design problem, and planning with a complex physics simulator. This paper proposes a new global optimization algorithm, called Locally Oriented Global Optimization (LOGO), to aim for both fast convergence in practice and finite-time error bound in theory. The advantage and usage of the new algorithm are illustrated via theoretical analysis and an experiment conducted with 11 benchmark test functions. Further, we modify the LOGO algorithm to specifically solve a planning problem via policy search with continuous state/action space and long time horizon while maintaining its finite-time error bound. We apply the proposed planning method to accident management of a nuclear power plant. The result of the application study demonstrates the practical utility of our method.