Convergence of a Multi-Agent Projected Stochastic Gradient Algorithm for Non-Convex Optimization

We introduce a new framework for the convergence analysis of a class of distributed constrained non-convex optimization algorithms in multi-agent systems. The aim is to search for local minimizers of a non-convex objective function which is supposed to be a sum of local utility functions of the agen...

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Vydáno v:IEEE transactions on automatic control Ročník 58; číslo 2; s. 391 - 405
Hlavní autoři: Bianchi, P., Jakubowicz, J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.02.2013
Institute of Electrical and Electronics Engineers
Témata:
Algorithm design and analysis
Computer Science
Convergence
Convergence of numerical methods
distributed algorithms
gradient methods
multiagent systems
Networking and Internet Architecture
Nickel
Noise
Optimization
Stochastic processes
Vectors
Gradient methods
Convergence of numerical methods
Multiagent systems
Distributed algorithms
ISSN:0018-9286, 1558-2523
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Popis
Shrnutí:We introduce a new framework for the convergence analysis of a class of distributed constrained non-convex optimization algorithms in multi-agent systems. The aim is to search for local minimizers of a non-convex objective function which is supposed to be a sum of local utility functions of the agents. The algorithm under study consists of two steps: a local stochastic gradient descent at each agent and a gossip step that drives the network of agents to a consensus. Under the assumption of decreasing stepsize, it is proved that consensus is asymptotically achieved in the network and that the algorithm converges to the set of Karush-Kuhn-Tucker points. As an important feature, the algorithm does not require the double-stochasticity of the gossip matrices. It is in particular suitable for use in a natural broadcast scenario for which no feedback messages between agents are required. It is proved that our results also holds if the number of communications in the network per unit of time vanishes at moderate speed as time increases, allowing potential savings of the network's energy. Applications to power allocation in wireless ad-hoc networks are discussed. Finally, we provide numerical results which sustain our claims.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2012.2209984