In this talk we consider the problem of temporal collaborative filtering where we consider the set of evolving rating matrices as a 3-D array or tensor. Using a class of structured tensor decompositions we first generalize notions of von Neumann entropy and divergence from positive definite matrices to positive definite tensors within this class. Using these notions we propose a generalization of matrix exponentiated gradient descent algorithm for learning psd matrices to a tensor exponentiated gradient descent algorithm for psd tensors. Then using a construction similar to (Hazan et al., 2012), we exploit this algorithm to propose an online algorithm  for learning and prediction of 3-D tensors with provable regret guarantees. Simulation results are presented on synthetic data sets.