Predictive state representations (PSRs) are a commonly used approach for agents to sum- marize the information from history generated during their interaction with a dynamical environment and the agents may use PSRs to predict the future observation. Existing works have shown the bene ts of PSRs for modelling partially observable dynamical systems. One of the key issues in PSRs is to discover a set of tests for representing states, which is called core tests. However, there is no very e cient technique to nd the core tests for a large and complex problem in practice. In this paper, we formulate the discovering of the set of core tests as an optimization problem and exploit a group sparsity of the decision-making matrix to solve the problem. Then the PSR parameters can be obtained simultaneously. Hence, the model of the underlying system can be built immediately. The new learning approach doesn't require the speci cation of the number of core tests. Furthermore, the embedded optimization method for solving the considered group Lasso problem, called alternating direction method of multipliers (ADMM), can achieve a global convergence. We conduct experiments on three problem domains including one extremely large problem domain and show promising performances of the new approach.