A0631
Title: A new approach to optimal design under model uncertainty motivated by multi-armed bandits
Authors: Mingyao Ai - Peking University (China)
Holger Dette - Ruhr-Universitaet Bochum (Germany)
Zhengfu Liu - Beijing Institute of Technology (China) [presenting]
Jun Yu - Beijing Institute of Technology (China)
Abstract: Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common for a researcher to have a list of candidate models at hand, and a design that is efficient for both model discrimination and parameter estimation in the (unknown) true model has to be found. A reinforcement learning approach is used to achieve a balance between these competing goals in the design of experiments. A sequential algorithm is developed to provide a design that has asymptotically the same performance as an optimal design when the true model could be correctly specified in advance. A lower bound is established to quantify the relative efficiency between such a design and an optimal design for the true model in finite stages. Moreover, the resulting designs are also efficient for discriminating between the true model and other rival models from the candidate list. Some connections with other state-of-the-art algorithms for model discrimination and parameter estimation are discussed, and the methodology is illustrated by a small simulation study.
