Dic: undeterred by something

• Undeterred by his early failures, he decided to keep writing.
• Even though most traders thrived under these autonomous conditions, there were few formal management constraints for those undeterred by the firm's culture. (modulated from another source)

If you are undeterred by something, you do not allow it to stop you doing what you want.

... LDOCE, http://www.ldoceonline.com/dictionary/undeterred