1. A weighting factor learning system comprising: an audio recognition section that recognizes learning audio data and outputting the recognition result; a weighting factor updating section that updates a weighting factor applied to a score obtained from an acoustic model and a language model which are used in audio recognition so that the difference between a correct-answer score calculated with the use of a correct-answer text of the learning audio data and a score of the recognition result output from the audio recognition section becomes large; a convergence determination section that determines, with the use of the score after updating, whether to return to the weighting factor updating section to update the weighting factor again; and a weighting factor convergence determination section that determines, with the use of the score after updating, whether to return to the audio recognition section to perform the process again and update the weighting factor using the weighting factor updating section.