repentance teshuvah - Someone in authority apologizes?

I am looking for examples where someone in authority apologizes to someone lower than him. I am specifically looking for examples where we know that the authority figure is someone to emulate (eg. the story is brought in the gemara, or in a mussar work, etc.).

For example did Hashem ever apologize?
How about a King?
How about others?

Examples please

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Edit

Still looking for an answer.
(DanF's answer does not show that Rav Elazar had authority,
b-a's answer does not show an explicit apology only a repayment for damages an implicit one,
mbloch's answer is an answer but it is possible that the child was not under the Steipler's authority,
Alex's answer clearly is saying that you need to apologize to a friend/neighbour and not regarding someone subordinate to you,
Gary's answer it seems pharoah by apologizing accepted the authority of G-d and Moses not that he was not apologizing from a position of authority.)