Kumārila dedicated to arthāpatti eighty-eight verses in his Ślokavārttika (which is a commentary on the epistemological section of the Śābarabhāṣya). One would expect that also his Bṛhaṭṭīkā, which comments on the same text, contained a portion on arthāpatti and this is indirectly confirmed by further evidences:

1. The verse said to be extracted from the Bṛhaṭṭīkā in the Mānameyoda‘s section on arthāpatti (discussed here)
2. Four verses on arthāpatti attributed by Śālikanātha* to the Vārttikakāra (i.e., Kumārila) but not found in his Ślokavārttika

All these texts agree, among other things, on a major distinction between inference and arthāpatti, namely the fact that the vyāpti, the ‘invariable concomitance’ between what will be known and its logical reason, is already at the epistemic disposal of the knower before the anumāna, whereas in the case of the arthāpatti the knower, so to say, discovers it “on the go”, at the time of reaching the result of the arthāpatti. In other words, one would not have been able to say beforehand that there is an invariable concomitance between the set of people who, being alive, are not at home, and the set of people who are out of their home, until one had reached the conclusion that Devadatta must be outside.

For further details, see Yoshimizu 2007 (in Preisendanz (ed.) Expanding and Merging Horizons).

*I am obliged to Kiyotaka Yoshimizu who kindly alerted me to these verses.