Theoretical Limits on the Success of Lexicase Selection Under Contradictory Objectives

Lexicase selection is a state of the art parent selection technique for problems that can be broken down into multiple selection criteria. Prior work has found cases where lexicase selection fails to find a Pareto-optimal solution due to the presence of multiple objectives that contradict each other. In other cases, however, lexicase selection has performed well despite the presence of such objectives. Here, we develop theory identifying circumstances under which lexicase selection will or will not fail to find a Pareto-optimal solution. Ultimately, we find that lexicase selection can perform well under many circumstances involving contradictory objectives, but that there are limits to the parameter spaces where high performance is possible. Additionally, we show empirical evidence that epsilon-lexicase selection is much more strongly impacted by contradictory objectives. Our results inform parameter value decisions under lexicase selection and decisions about which problems to use lexicase selection for.