Generalisation and Domain Adaptation in GP with Gradient Descent for Symbolic Regression

Genetic programming (GP) has been widely applied to symbolic regression problems and achieved good success. Gradient descent has also been used in GP as a complementary search to the genetic beam search to further improve symbolic regression performance. However, most existing GP approaches with gradient descent (GPGD) to symbolic regression have only been tested on the "conventional" symbolic regression problems such as benchmark function approximations and engineering practical problems with a single (training) data set only and the effectiveness on unseen data sets in the same domain and in different domains has not been fully investigated. This paper designs a series of experiment objectives to investigate the effectiveness and efficiency of GPGD with various settings for a set of symbolic regression problems applied to unseen data in the same domain and adapted to other domains. The results suggest that the existing GPGD method applying gradient descent to all evolved program trees three times at every generation can perform very well on the training set itself, but cannot generalise well on the unseen data set in the same domain and cannot be adapted to unseen data in an extended domain. Applying gradient descent to the best program in the final generation of GP can also improve the performance over the standard GP method and can generalise well on unseen data for some of the tasks in the same domain, but perform poorly on the unseen data in an extended domain. Applying gradient descent to the top 20% programs in the population can generalise reasonably well on the unseen data in not only the same domain but also in an extended domain.