In digital markets comprised of many compet-ing services, user chooses between multiple ser-vice providers according to their preferences, andthe chosen service makes use of the user datato incrementally improve its model. The serviceproviders’ models influence which service theuser will choose at the next time step, and theuser’s choice, in return, influences the model up-date, leading to a feedback loop. In this paper, weformalize the above dynamics and develop a sim-ple and efficient decentralized algorithm to locallyminimize the overall user loss. Theoretically, weshow that our algorithm asymptotically convergesto stationary points of of the overall loss almostsurely. We also experimentally demonstrate theutility of our algorithm with real world data.