We study how to infer the couplings exactly in a non-equilibrium asynchrnously updated Ising model from the observed spin history. This simple example contains two types of stochastic processes: spin configrations which is visiable and the updating time of the spins which is hidden. We devided the learning rule for the couplings and the external field by minimizing the log-likelihood of the data. And there are two ways to deal with the unobserved variables in general. The reconstructed error for these learning rules are calculated. Besides, with the property that L1 regularization tends to provide sparse solutions, we rewrite the cost function as summation of negative log-likelihood and L1 norm term with regularization parameter $lambda$. And try to minimize the cost function for given $lambda$ value by simple graident decent algorithm. The additional term gives a penalty term to the corresponding exact learning rules. We apply such L1 regularization to a diluted and binary network and try to eliminate the least significant couplings (actually zero bonds). The classification errors with differnet $lambda$ values are studied.