Measuring interestingness of continuous game problems

This paper investigates the relationship between the difficulty and the interestingness of individual problem candidates from within a class of related problems, using Lunar Lander as a case study. In this class of problems, a 2D spaceship must be controlled by a simple set of macro-actions, including both linear and angular impulses, such that it fulfils a set of weighted criteria relating to landing on a jagged landscape with flat landing pads. It is demonstrated that a very simple measure based on standard deviations of improvement can be used to guide evolution to develop interesting problems in this class of problems, which in turn can be solved using evolution strategies to get a high level of improvement based on initial random performance. We examine the impact of the measure used on the evolution of the problems, and also what aspects of this problem class affect the difficulty and interestingness the most.