Active learning with adaptive grids

Given some optimization problem and a series of typically expensive trials of solution candidates taken from a search space, how can we efficiently select the next candidate? We address this fundamental problem using adaptive grids inspired by Kohonen’s self-organizing map. Initially the grid divides the search space into equal simplexes. To select a candidate we uniform randomly first select a simplex, then a point within the simplex. Grid nodes are attracted by candidates that lead to improved evaluations. This quickly biases the active data selection process towards promising regions, without loss of ability to deal with”surprising” global optima in other areas. On standard benchmark functions the technique performs more reliably than the widely used covariance matrix adaptation evolution strategy.