Many applications in multiagent learning are essentially convex optimization problems in which agents have only limited communication and partial information about the function being minimized (examples of such applications include, among others, coordinated source localization, distributed adaptive filtering, control, and coordination). Given this observation, we propose a new non-hierarchical decentralized algorithm for the asymptotic minimization of possibly time-varying convex functions. In our method each agent has knowledge of a time-varying local cost function, and the objective is to minimize asymptotically a global cost function defined by the sum of the local functions. At each iteration of our algorithm, agents improve their estimates of a minimizer of the global function by applying a particular version of the adaptive projected subgradient method to their local functions. Then the agents exchange and mix their improved estimates using a probabilistic model based on recent results in weighted average consensus algorithms. The resulting algorithm is provably optimal and reproduces as particular cases many existing algorithms (such as consensus algorithms and recent methods based on the adaptive projected subgradient method). To illustrate one possible application, we show how our algorithm can be applied to coordinated acoustic source localization in sensor networks
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