Distributed multi-agent optimization with state-dependent communication |
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Authors: | Ilan Lobel Asuman Ozdaglar Diego Feijer |
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Institution: | (1) Stern School of Business, New York University, New York, NY, USA;(2) Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA |
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Abstract: | We study distributed algorithms for solving global optimization problems in which the objective function is the sum of local
objective functions of agents and the constraint set is given by the intersection of local constraint sets of agents. We assume
that each agent knows only his own local objective function and constraint set, and exchanges information with the other agents
over a randomly varying network topology to update his information state. We assume a state-dependent communication model over this topology: communication is Markovian with respect to the states of the agents and the probability with which the
links are available depends on the states of the agents. We study a projected multi-agent subgradient algorithm under state-dependent communication. The state-dependence of the communication introduces significant challenges and couples
the study of information exchange with the analysis of subgradient steps and projection errors. We first show that the multi-agent
subgradient algorithm when used with a constant stepsize may result in the agent estimates to diverge with probability one.
Under some assumptions on the stepsize sequence, we provide convergence rate bounds on a “disagreement metric” between the
agent estimates. Our bounds are time-nonhomogeneous in the sense that they depend on the initial starting time. Despite this,
we show that agent estimates reach an almost sure consensus and converge to the same optimal solution of the global optimization
problem with probability one under different assumptions on the local constraint sets and the stepsize sequence. |
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