Modified Error Bounds for Matrix Completion and Application to RL

In matrix completion under noisy measurements, most available results assume that there is an a priori bound on the Frobenius norm of the noise, and derive bounds on the Frobenius norm of the residual error. In this letter, we obtain "component-wise" bounds on the residual error, based on a similar bound on the noise. This among the first such results. As in our earlier paper, choose the locations of the samples to correspond to the edge set of a Ramanujan bigraph. One recent application is to deriving nearly optimal action-value functions in Reinforcement Learning (RL), which is illustrated through examples. The results presented here are only sufficient conditions. Then we illustrate through numerical simulations that there is considerable room for improvement in the sufficient conditions derived here. This is a problem for future research.