We consider the optimal learning problem of optimizing an expensive function f(x; θ) with a known parametric form but unknown parameter vector θ. Observations of the function, which might involve simulations or laboratory or field experiments, are both expensive and noisy. Our goal is to simultaneously learn the true parameter θ while finding the optimal value of x. We develop an efficient implementation of a method, known as the knowledge gradient, that optimizes the value of information from each experiment. Our algorithm can handle x and θ that are multidimensional continuous vectors. We prove that our algorithm asymptotically learns the correct θ and the best value of x. Experiments show that the algorithm produces fast convergence, even in higher dimensions.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Knowledge gradient
- Nonlinear parametric model
- Optimal learning