Evolving simple and accurate symbolic regression models via asynchronous parallel computing

Abstract

In machine learning, reducing the complexity of a model can help to improve its computational efficiency and avoid overfitting. In genetic programming (GP), the model complexity reduction is often achieved by reducing the size of evolved expressions. However, previous studies have demonstrated that the expression size reduction does not necessarily prevent model overfitting. \n \nTherefore, this paper uses the evaluation time --- the computational time required to evaluate a GP model on data --- as the estimate of model complexity. \nThe evaluation time depends not only on the size of evolved expressions but also their composition, thus acting as a more nuanced measure of model complexity than the expression size alone. \nTo discourage complexity, this study employs a novel method called asynchronous parallel GP (APGP) that introduces a race condition in the evolutionary process of GP; the race offers an evolutionary advantage to the simple solutions when their accuracy is competitive. \n \n \nTo evaluate the proposed method, it is compared to the standard GP (GP) and GP with bloat control (GP+BC) methods on six challenging symbolic regression problems. APGP produced models that are significantly more accurate (on 6/6 problems) than those produced by both GP and GP+BC. In terms of complexity control, APGP prevailed over GP but not over GP+BC; however, GP+BC produced simpler solutions at the cost of test-set accuracy. Moreover, APGP took a significantly lower number of evaluations than both GP and GP+BC to meet a target training fitness in all tests. \n \n \nOur analysis of the proposed APGP also involved: (1) an ablation study that separated the proposed measure of complexity from the race condition in APGP and (2) the study of an initialization scheme that encourages functional diversity in the initial population that improved the results for all the GP methods. \n \n \nThese results question the overall benefits of bloat control and endorse the employment of both the evaluation time as an estimate of model complexity and the proposed APGP method for controlling it.