Level Set Estimation with Search Space Warping

This paper proposes a new method of level set estimation through search space warping using Bayesian optimisation. Instead of a single solution, a level set offers a range of solutions each meeting the goal and thus provides useful knowledge in tolerance for industrial product design. The proposed warping scheme increases performance of existing level set estimation algorithms in particular the ambiguity acquisition function. This is done by constructing a complex covariance function to warp the Gaussian Process. The covariance function is designed to expand regions deemed to have a high potential for being at the desired level whilst contracting others. Subsequently, Bayesian optimisation using this covariance function ensures that the level set is sampled more thoroughly. Experimental results demonstrate increased efficiency of level set discovery using the warping scheme. Theoretical analysis concerning warping the covariance function, maximum information gain and bounds on the cumulative regret are provided.