This study focuses on dynamical system identification, with the reverse modeling of a gene regulatory network as motivating appli-cation. An active learning approach is used to iteratively select the most informative experiments needed to improve the parameters and hidden variables estimates in a dynamical model given a budget for experiments. The design of experiments under these budgeted resources is formalized in terms of sequential optimization. A local optimization criterion (re-ward) is designed to assess each experiment in the sequence, and the global optimization of the sequence is tackled in a game-inspired setting, within the Upper Confidence Tree framework combining Monte-Carlo tree-search and multi-armed bandits. The approach, called EDEN for Experimental Design for parameter Estimation in a Network, shows very good performances on several re-alistic simulated problems of gene regulatory network reverse-modeling, inspired from the international challenge DREAM7.