SC²S Colloquium - May 13, 2015

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Date: May 13, 2015
Room: 02.07.023
Time: 3:00 pm, s.t.

Evangelos Drossos: Bayesian Multi-scale Optimistic Optimization with Adaptive Sparse Grids

Global function optimization is a common problem in a wide range of disciplines. The optimization of functions in higher-dimensions can become particularly costly, as the number of function evaluations required by most optimization techniques rises exponentially in the number of dimensions. This paper examines a Bayesian optimistic optimization technique that employs a tree-based approach to determine the maximum of a (multi-)dimensional function, where promising nodes are further refined until a maximum tree depth is reached or a predetermined budget of function evaluations gets exhausted. The algorithm utilizes Gaussian process confidence bounds to identify nodes for further refinement, thereby eliminating the need for the optimization of an acquisition function. In an attempt to tackle the curse of dimensionality, this paper proposes some modifications to the base model to allow for the use of an adaptive sparse grid to represent function evaluations. Important aspects are considered, especially regarding the selection of grid points, the adaptivity method and the choice of the refinement criterium to fit the base model.