Adaptive Penalty-Based Distributed Stochastic Convex Optimization

• Published in: IEEE transactions on signal processing Vol. 62; no. 15; pp. 3924 - 3938
• Main Authors: Towfic, Zaid J., Sayed, Ali H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Adaptation and learning; Algorithms; Applied sciences; Approximation algorithms; Approximation methods; consensus strategies; Constants; constrained optimization; Convex functions; Cost engineering; Cost function; Detection, estimation, filtering, equalization, prediction; diffusion strategies; distributed processing; Exact sciences and technology; Information, signal and communications theory; Networks; Optimization; penalty method; Processors; Signal and communications theory; Signal processing algorithms; Signal, noise; Strategy; Telecommunications and information theory; Target tracking; Adaptation and learning; Adaptive algorithm; diffusion strategies; Network architecture; Stochastic method; Convex programming; Penalty method; Constrained optimization; Learning; Topological structure; Distributed processing; Optimal solution; Distributed algorithm; Signal processing; Cost function; consensus strategies; Convex function; Localization
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2014.2331615

In this work, we study the task of distributed optimization over a network of learners in which each learner possesses a convex cost function, a set of affine equality constraints, and a set of convex inequality constraints. We propose a fully distributed adaptive diffusion algorithm based on penalty methods that allows the network to cooperatively optimize the global cost function, which is defined as the sum of the individual costs over the network, subject to all constraints. We show that when small constant step-sizes are employed, the expected distance between the optimal solution vector and that obtained at each node in the network can be made arbitrarily small. Two distinguishing features of the proposed solution relative to other approaches is that the developed strategy does not require the use of projections and is able to track drifts in the location of the minimizer due to changes in the constraints or in the aggregate cost itself. The proposed strategy is able to cope with changing network topology, is robust to network disruptions, and does not require global information or rely on central processors.