ZOOpt: Toolbox for Derivative-Free Optimization

Recent advances of derivative-free optimization allow efficient approximating the global optimal solutions of sophisticated functions, such as functions with many local optima, non-differentiable and non-continuous functions. This article describes the ZOOpt (https://github.com/eyounx/ZOOpt) toolbox that provides efficient derivative-free solvers and are designed easy to use. ZOOpt provides a Python package for single-thread optimization, and a light-weighted distributed version with the help of the Julia language for Python described functions. ZOOpt toolbox particularly focuses on optimization problems in machine learning, addressing high-dimensional, noisy, and large-scale problems. The toolbox is being maintained toward ready-to-use tool in real-world machine learning tasks

Acoustic Lens Design Using Machine Learning

This thesis aims to contribute to the development of a novel approach and efficient method for the inverse design of acoustic metamaterial lenses using machine learning, specifically, deep learning, generative modeling, and reinforcement learning. Acoustic lenses can focus incident plane waves at the focal point, enabling them to detect structures non-intrusively. These lenses can be utilized in biomedical engineering, medical devices, structural engineering, ultrasound imaging, health monitoring, etc. Finding the global optimum through a traditional iterative optimization process for designing the acoustic lens is challenging. It may become infeasible due to high dimensional parameter space and the compute resources needed. Machine learning techniques have been shown promising for finding the global optimum. Generative modeling is a powerful technique enabling recent advancements in drug discoveries, organic molecule development, and photonics. We combined generative modeling with global optimization and an analytical form of gradients computed by means of multiple scattering theory. In addition, reinforcement learning can potentially outperform traditional optimization algorithms. Thus, in this thesis, the acoustic lens is modeled using two machine learning techniques, such as generative modeling, using 2D-Global Topology Optimization Networks (2D-GLOnets), and reinforcement learning using the Deep Deterministic Policy Gradient (DDPG) algorithm. Results from the aforementioned methods are compared with traditional optimization algorithms

Global Continuous Optimization with Error Bound and Fast Convergence

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