Rewarding Model Smoothness and Simplicity via Alternating Objectives in Symbolic Regression

We revisit the use of the Alternating Pareto Tournament selection strategy, which can efficiently optimize multiple independent fitness objectives. We explore how alternating objectives can be used to exploit a new model curvature estimator in search. We demonstrate this strategy can be used to effectively balance model complexity, accuracy, and model curvature. We further showcase how alternating objectives can be tuned to apply uneven fitness pressure on each objective by changing the frequency each objective is used across generations. We show that considering complexity and curvature during search can improve training efficiency while also improving generalization capabilities.