Feed, when used with a preposition, is most often used with on:
Tom seeks to escape from regularity by romanticism. He feeds on detective and adventure stories — James T. Farrell, The League of Frightened Philistines, 1945
When writing turns to mush, thought, which feeds on writing, suffers from malnutrition —Thomas H. Middleton, Saturday Rev., 24 Nov. 1979
Feed has also been used with upon or off. Although still less frequent than on, recent evidence suggests that the use of upon and off has been growing:
... to think again; to feed upon memory —Walter De la Mare, Encounter, December 1954
... shifted his stance toward his art and the experience that his art fed upon —Donald Davie, N.Y. Times Book Rev., 25 Apr. 1976
The dread of the new place mounts up in her and feeds off the complaints in his letters —Oscar Han-dlin, The Uprooted, 1951
... have the sort of hardcover sale that... the soft-cover could feed off the celebrity —N. R. KJeinfield, N.Y. Times Book Rev., 16 Sept. 1979
Feed may even occur with from, but this seems to be a far from usual combination:
(资料出处：韦伯斯特英语用法词典)... in a position to reward those who ... are content to feed from officially provided sources —Thomas B. Littlewood, Saturday Rev., 15 Apr. 1972