The high-speed rail is offering teens through the age of 18 years old discounts of 30-50 percent on select runs, from now through September 1. (NB: the discount does not apply to all tickets. Check the schedule.)
This applies only to tickets bought at the counter. So 7-Eleven Ibons, etc., won't work for this. A photo ID is needed to verify age.
source (in Mandarin): 12 suì yǐshàng wèimǎn 19 suì shàonián dā gāotiě Běi-Gāo zuìdī 5 zhé qǐ