Collaborative Filtering via Online Mirror Descent

In this report, we will study online learning algorithms, and in particular, online mirror descent (OMD) method when applied to the collaborative filtering problem. This is motivated by the problem of real-world large-scale recommendation systems, where the goal is to make relevant recommendations to the users based on their demographic information, their past behavior, and the other users’ bahevior. In order to analyze regret bounds of OMD on this problem, we need to equip ourselves with tools from convexity analysis for matrices. We will compare our results to the baseline result and observe a substantial improvement in the regret function.