Open Access Open Access  Restricted Access Subscription or Fee Access

A Learning Procedure for Sampling Semantically Different Valid Expressions

David L. St-Pierre, Francis Maes, Damien Ernst, Quentin Louveaux


A large number of problems can be formalized as finding the best symbolic expression to maximize a given numerical objective. Most approaches to approximately solve such problems rely on random exploration of the search space. This paper focuses on how this random exploration should be performed to take into account expressions redundancy and invalid expressions. We propose a learning algorithm that, given the set of available constants, variables and operators and given the target finite number of trials, computes a probability distribution to maximize the expected number of semantically different, valid, generated expressions. We illustrate the use of our approach on both medium scale and large-scale expression spaces, and empirically show that such optimized distributions significantly outperform the uniform distribution in terms of the diversity of generated expressions.

We further test the method in combination with the recently proposed nested Monte Carlo algorithm on a set of benchmark symbolic regression problems and demonstrate its interest in terms of reduction of the number of required calls to the objective function.


Symbolic Regression, Machine Learning, optimization.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.