All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ʻalayhi wa sallam, is His Slave and Messenger.
If you mean that you promised him in the name of Allaah to do a given act, then you are obligated to honor your commitment. Allaah The Exalted says (what means): {And fulfill (every) commitment. Indeed, the commitment is ever (that about which one will be) questioned.} [Quran 17:34] The Prophet, sallallaahu ʻalayhi wa sallam, warned against breaking promises and declared it to be one of the characteristics of the hypocrites. He, sallallaahu ʻalayhi wa sallam, said: “A person who has these four (characteristics) is a pure hypocrite and he who possesses one of them has a trait of hypocrisy until he abandons it: when he talks, he lies; when he makes a covenant, he proves to be treacherous; when he makes a promise, he breaks it; and when he disagrees with others, he disputes violently.” [Al-Bukhari and Muslim]
The obligation is perhaps even more emphasized with regards to the father with his child and the leader with his people so they do not develop an aversion towards him because of him breaking his commitments or so they do not take him as a bad example.
Al-Maawardi said: “The king should know that fulfilling his covenants is one pillar upon which his sovereignty is based; verily, breach of covenants is a blameworthy quality and it is even more blameworthy on the part of the king or ruler and more detrimental to him because the ruler who is not trusted to honor his covenants, whose actions do not agree with his words, and who is known for breaking his agreements and covenants, would find great difficulty in having his people submit to his rule and there would be great aversion towards him.” [Tas-heel An-Nathar]
Regarding the expiation, the jurists disagreed about one who declares to Allaah his commitment to do something, whether it is an oath (Yameen), or whether it is a vow (Nathr) and an oath as well, or whether he is not obligated to do anything. Please refer to Fatwa 118909.
Since what you have committed yourself to do is not an act of worship that draws a person closer to Allaah, then it is an oath. Please refer to Fatwa 87181 about the expiation for breaking an oath.
Allaah Knows best.