Convergence analysis for an online recommendation system

Online recommendation systems use votes from experts or other users to recommend objects to customers. We propose a recommendation algorithm that uses an average weight updating rule and prove its convergence to the best expert and derive an upper bound on its loss. Often times, recommendation algorithms make assumptions that do not hold in practice such as requiring a large number of the good objects, presence of experts with the exact same taste as the user receiving the recommendation, or experts who vote on all or majority of objects. Our algorithm relaxes these assumptions. Besides theoretical performance guarantees, our simulation results show that the proposed algorithm outperforms current state-of-the-art recommendation algorithm, Dsybil.