The discharge current and potential difference between cathode and ground of a Hall thruster were predicted sequentially by Recurrent Neural Network (RNN) in order to optimize operating conditions. The prediction accuracy and calculation cost for three RNN models, the standard Echo State Network (simpleESN), cycle-groupedESN, and Long Short-Term Memory (LSTM) were compared. The ESN model structures were chosen using Bayesian optimization. We calculated the normalized root mean square error (NRMSE) of the model output against the experimental results of a 200 W class Hall thruster developed at Kyushu University. The NRMSE of the simpleESN model output against discharge current was 0.0407, about 1/10 that of the LSTM. The NRMSE of the simpleESN model against the potential difference between cathode and ground was 0.0981, about 1/7 that of the LSTM. Moreover, cycle-groupedESN reduced the calculation time for the optimization process to 24 seconds, compared to 303 seconds with simpleESN, though the NRMSE against discharge current of the cycle-grouped ESN was 0.1179. These results show that the simpleESN and cycle-groupedESN models are superior to the LSTM in both prediction accuracy and calculation costs for prediction of discharge current and voltage between ground and cathode in Hall thrusters in the considered settings.