Scalable and Reliable Optimization of Expensive Multi-Modal Functions: A Bayesian Perspective
Abstract
Optimization is pervasive in scientific and industrial endeavors for purposes including resource management, autonomous maneuverability, design and control of adaptive and resilient intelligent systems, developing next-generation munitions, combat training, and adaptable resilient disaster response. A large number of these real-world problems can be considered as multi-modal optimization, where it is desired to find all or most global and local optimum solutions as implementing some of the optimal solutions might not be feasible due to various practical restrictions (i.e., resource limitation, physical constraints, etc.). Meanwhile, the objective functions are often computationally or economically expensive, and the optimization is associated with multiple sources of uncertainty such as low-fidelity/approximate function evaluation, input uncertainty, or sensor/technological noises. The existing multi-modal optimization techniques do not provide any analysis of convergence to global/local optimum and come short to deal with realistic multi-modal objective functions due to reliance on heuristics, on excessive function evaluations, and on exact evaluation of objective functions. The primary goal of this proposal is to develop Bayesian optimization frameworks capable of efficient, reliable, and scalable optimization of expensive multi-modal functions. The proposed research will significantly advance state of art in multi-modal optimization and contribute to the science base of machine learning, decision/learning theory, and Bayesian statistics. Original contributions are expected in: (i) Multi-Modal Bayesian Optimization: This project will develop multi-modal Bayesian optimization frameworks capable of efficiently computing a set of optimum solutions. The proposed frameworks will be built on various Bayesian models (e.g., Gaussian process regression, Bayesian graphical models, and Bayesian neural networks) and will enable efficient optimization of complex multi-modal objectives in arbitrary search spaces through multiple fidelity models and in non-stationary domains. (ii) Large-Scale Bayesian Optimization: We will introduce linear and nonlinear dimensionality reduction Bayesian optimization frameworks for efficient and reliable optimization in high-dimensional spaces. The proposed frameworks will map the original high-dimensional space to a lower-dimensional design space in which much more efficient and informative optimization can be achieved. (iii) Lookahead Bayesian Optimization: Toward overcoming the greedy (one-step lookahead) search in most of the existing Bayesian optimization techniques, this project will provide a unified Markov decision process (MDP) formulation of Bayesian optimization techniques and will develop near-optimal finite and infinite horizon Bayesian optimization frameworks capable of dealing with expensive multi-modal objective functions. (iv) Expert-Enabled Bayesian Optimization: To account for expert/prior knowledge in the optimization process, this project will take advantage of the MDP formulation of the Bayesian optimization policies to develop inverse reinforcement learning Bayesian optimization frameworks capable of scalable, reliable and efficient quantification of experts /prior knowledge and integrating them in the optimization process. All the developed tools in this project will be presented in a user-friendly software/tool freely accessible to other researchers.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 07, 2021
- Source ID
- W911NF2110299
Entities
People
- Mahdi Imani
Organizations
- Army Contracting Command
- George Washington University
- United States Army