He studies on his own initiative.

他学习很自觉。

《新英汉大辞典》

Did he do it on his own initiative?

他是自己主动做的吗？

youdao

He developed the plan on his own initiative.

他主动制定了该计划。

youdao

The report also found that Jack Ruby, 53, who shot Oswald dead two days after the president's death at a Dallas police station also acted on his own initiative.

BBC: 28 September

And we have there the explicit instructions for the head of Bomber Command, if the Prime Minister's wiped out, and he can't find an alternative senior minister, the airman, on his own initiative, can launch retaliation.

BBC