Multi-fidelity Modeling With Varying Costs Using Optimal Learning

Abstract

Running experiments and simulations can be very expensive. Efficient usage of resources is prevalent and applicable to many industries such as financial services, pharmaceuticals, and transportation systems. Within varying levels of experimentation, there is a trade-of between cost and accuracy. By supplementing such high-fidelity and high cost models with low-fidelity cheaper models in a multi-fidelity model, higher accuracy can be achieved at lower cost. This paper provides a framework for approaching such problems. We give a method of combining different sources of data from multivariate normal models. The Knowledge Gradient is adapted to this context using the methodology from the Hierarchical Knowledge Gradient. A proof of convergence of the multi-fidelity Knowledge Gradient on independent beliefs is given. A setup for simulation is provided in order to test the robustness of the model to varying forms of approximation and determine how the multi-fidelity knowledge gradient compares to other heuristics such as Expected Improvement. By using the appropriate heuristic for the task at hand, Optimal Learning allows for improved efficiency in the usage of resources.