GAME: Genetic Algorithms with Marginalised Ensembles for model-independent reconstruction of cosmological quantities

Genetic Algorithms (GA) are a powerful tool for stochastic optimisation and non-parametric symbolic regression, already widely used in cosmology. They are capable of reconstructing analytical functions directly from data points without introducing new physical models. A limitation of this approach is that while the reconstructed function is very efficient at reproducing the behaviour of the data points, non-observable quantities involving derivatives are particularly sensitive to stochasticity, hyperparameters, and to the choice of the best-fit function obtained by the GA, which implies the risk of the algorithm getting stuck in a local minimum. In this work we propose an update to the GA methodology for the reconstruction of analytical functions that involves computing a weighted average of an ensemble of GA configurations (\texttt{GAME}). We define the weights via a quantity that accounts for both the goodness-of-fit of the points and the smoothness of the resulting function. We also present a practical method to analytically estimate and correct the errors on the averaged function by combining a path-integral approach with an ensemble variance. We demonstrate the improvement offered by \texttt{GAME} methodology on a generic test function. We then apply the new methodology to a non-parametric reconstruction of the Hubble rate $H(z)$ using Cosmic Chronometers data and, assuming a flat Friedmann-Lema\^itre-Robertson-Walker background and General Relativity, we infer the corresponding dark energy equation of state $w(z)$. Through consistency tests, we show that current data produces results compatible with $\Lambda$CDM, and that Stage IV cosmology surveys will allow GA reinforced with \texttt{GAME} methodology to become an even more competitive tool for discriminating between different models.