Jamieson, Fausset and Brown on Jeremiah 31:2

2. Upon the grace manifested to Israel "in the wilderness" God grounds His argument for renewing His favors to them now in their exile; because His covenant is "everlasting" (Jr 31:3), and changes not. The same argument occurs in Ho 13:5, 9, 10; 14:4, 5, 8. Babylon is fitly compared to the "wilderness," as in both alike Israel was as a stranger far from his appointed "rest" or home, and Babylon is in Is 40:3 called a "desert" (compare Jr 50:12).

I went to cause him to rest--namely, in the pillar of cloud and fire, the symbol of God's presence, which went before Israel to search a resting-place (Nu 10:33; Is 63:14) for the people, both a temporary one at each halt in the wilderness, and a permanent one in Canaan (Ex 33:14; De 3:20; Jos 21:44; Psa 95:11; He 3:11).