Multi-Task Semantic Genetic Programming With Reinforcement Learning for Multi-Output Symbolic Regression

Multi-output symbolic regression involves predicting two or more target variables simultaneously, adding complexity compared to single-output symbolic regression due to the interdependence between target variables. These dependencies require careful consideration of the relationships between outputs to improve prediction accuracy. It can be treated as a specific form of multi-task optimization, where tasks share the same input variables but predict different output variables. The main challenge lies in determining the optimal intensity of knowledge transfer, selecting relevant tasks, and extracting valuable knowledge during the evolutionary process. To tackle these challenges, we propose a new multi-task multi-population genetic programming method that incorporates reinforcement learning and a semantics-based transfer strategy. Specifically, reinforcement learning adaptively adjusts transfer intensity, selects similar tasks and determines the most valuable genetic materials for effective knowledge transfer. The semantics-based transfer strategy with cosine similarity identifies the most informative knowledge from similar tasks to generate high-quality offspring. Empirical results on 18 real-world datasets show that our proposed method significantly improves the training and test performance of multi-task GP, surpassing state-of-the-art multi-task GP methods on most examined datasets.