d(Tree)-by-dx: automatic and Exact Differentiation of Genetic Programming Trees

• Peter Rockett ^[1] ; Yuri Kaszubowski Lopes ^[1] ; Tiantian Dou ^[1] ; Hathway, Elizabeth A. ^[1]
  1. [1] University of Sheffield

     University of Sheffield

     Reino Unido

     
• Localización: Hybrid Artificial Intelligent Systems. 14th International Conference, HAIS 2019: León, Spain, September 4–6, 2019. Proceedings / coord. por Hilde Pérez García, Lidia Sánchez González, Manuel Castejón Limas, Héctor Quintián Pardo, Emilio Santiago Corchado Rodríguez, 2019, ISBN 978-3-030-29858-6, págs. 133-144
• Idioma: inglés
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• Resumen

  • Genetic programming (GP) has developed to the point where it is a credible candidate for the ‘black box’ modeling of real systems. Wider application, however, could greatly benefit from its seamless embedding in conventional optimization schemes, which are most efficiently carried out using gradient-based methods. This paper describes the development of a method to automatically differentiate GP trees using a series of tree transformation rules; the resulting method can be applied an unlimited number of times to obtain higher derivatives of the function approximated by the original, trained GP tree. We demonstrate the utility of our method using a number of illustrative gradient-based optimizations that embed GP models.