In-network Nonconvex Large-scale Optimization

Gesualdo Scutari
Purdue University

Nowadays, large-scale systems are ubiquitous. Some examples/applications include wireless communication networks; electricity grid, sensor, and cloud networks; and machine learning and signal processing applications, just to name a few. In many of the above systems, i) data are distributively stored in the network (e.g., clouds, computers, sensors, robots), and ii) it is often impossible to run analytics on central fusion centers, owing to the volume of data, energy constraints, and/or privacy issues. Thus, distributed in-network processing with parallelized multi-processors is preferred. Moreover, many applications of interest lead to large-scale optimization problems with nonconvex, nonseparable objective functions. All this makes the analysis and design of distributed/parallel algorithms over networks a challenging task.
In this talk we will present our ongoing work in this area. More specifically, we consider a large-scale network composed of agents aiming to distributively minimize a (nonconvex) smooth sum-utility function plus a nonsmooth (nonseparable), convex one. The latter is usually employed to enforce some structure in the solution, e.g., sparsity. The agents have access only to their local functions (data) but not the whole objective, and the network is modeled as a directed, time-varying, graph. We propose a distributed solution method for the above optimization wherein the agents in parallel minimize a convex surrogate of the original nonconvex objective while using a novel tacking mechanism and broadcast protocol to estimate locally the missing global information and distribute the computations over the network, respectively. We discuss several instances of the general algorithm framework tailored to specific (convex and nonconvex) applications and present some numerical results validating our theoretical findings.

Bio: Gesualdo Scutari is an Associate Professor with the School of Industrial Engineering at Purdue University and is the Scientific Director for the area of Big-Data Analytics at the Cyber Center (Discovery Park) at Purdue University. His primary research interests focus on theoretical and algorithmic issues related to continuous (large-scale) optimization, Big-Data Analytics, equilibrium programming, and their applications to signal processing, communications, and machine learning. He is an Associate Editor of the IEEE Transactions on Signal Processing.

He received several awards including the 2013 NSF CAREER Award and the 2015 IEEE Signal Processing Society Young Author Best Paper Award.

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