A General Analysis of the Convergence of ADMM

We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms introduced in Lessard et al. (2014), reducing algorithm convergence to verifying the stability of a dynamical system. This approach generalizes a number of existing results and obviates any assumptions about specific choices of algorithm parameters. On a numerical example, we demonstrate that minimizing the derived bound on the convergence rate provides a practical approach to selecting algorithm parameters for particular ADMM instances. We complement our upper bound by constructing a nearly-matching lower bound on the worst-case rate of convergence.Comment: 10 pages, 6 figure

Temporal Model Adaptation for Person Re-Identification

Person re-identification is an open and challenging problem in computer vision. Majority of the efforts have been spent either to design the best feature representation or to learn the optimal matching metric. Most approaches have neglected the problem of adapting the selected features or the learned model over time. To address such a problem, we propose a temporal model adaptation scheme with human in the loop. We first introduce a similarity-dissimilarity learning method which can be trained in an incremental fashion by means of a stochastic alternating directions methods of multipliers optimization procedure. Then, to achieve temporal adaptation with limited human effort, we exploit a graph-based approach to present the user only the most informative probe-gallery matches that should be used to update the model. Results on three datasets have shown that our approach performs on par or even better than state-of-the-art approaches while reducing the manual pairwise labeling effort by about 80%