Learning Consistent Causal Abstractions with Genetic Algorithms

Recent work in machine learning and artificial intelligence has dealt with bringing together two fundamental concepts underlying intelligence: causality and abstraction. Given two SCMs representing the same system at different levels of detail, learning an abstraction between them turned out to be a hard combinatorial problem, and solutions have been proposed relying on neural networks and optimal transport. In this paper, we consider the original problem of abstraction learning and we generalize it. We start highlighting a connection to the standard bin packing problem, and then we show that the problem at hand is actually an instance of a larger class of non-decomposable product of combinatorial problems. We propose an approach to solving these problems relying on genetic algorithms. Compared with a gradient descent approach, genetic algorithms do not require a relaxation of the problem and they can explore different regions of the solution space without getting stuck in sub-optimal minima. Furthermore, we will also show that the compositional form of the problem suits well the schemata hypothesis for genetic algorithm.